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Courbes Semi Stables Et Groupe Fondamental En Geometrie Algebrique
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Book Synopsis Courbes semi-stables et groupe fondamental en geometrie algebrique by : Jean-Benoit Bost
Download or read book Courbes semi-stables et groupe fondamental en geometrie algebrique written by Jean-Benoit Bost and published by Springer Science & Business Media. This book was released on 2000-08-01 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains detailed expositions of talks given during an instructional conference held at Luminy in December 1998, which was devoted to classical and recent results concerning the fundamental group of algebraic curves, especially over finite and local fields. The scientific guidance of the conference was supplied by M. Raynaud, a leading expert in the field. The purpose of this volume is twofold. Firstly, it gives an account of basic results concerning rigid geometry, stable curves, and algebraic fundamental groups, in a form which should make them largely accessible to graduate students mastering a basic course in modern algebraic geometry. However classic, most of this material has not appeared in book form yet. In particular, the semi-stable reduction theorem for curves is covered with special care, including various detailed proofs. Secondly, it presents self-contained expositions of important recent developments, including the work of Tamagawa on Grothendieck's anabelian conjecture for curves over finite fields, and the solution by Raynaud and Harbater of Abhyankar's conjecture about coverings of affine curves in positive characteristic. These expositions should be accessible to research students who have read the previous chapters. They are also aimed at experts in number theory and algebraic geometry who want to read a streamlined account of these recent advances.
Book Synopsis Arithmetic and Geometry Around Galois Theory by : Pierre Dèbes
Download or read book Arithmetic and Geometry Around Galois Theory written by Pierre Dèbes and published by Springer Science & Business Media. This book was released on 2012-12-13 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Lecture Notes volume is the fruit of two research-level summer schools jointly organized by the GTEM node at Lille University and the team of Galatasaray University (Istanbul): "Geometry and Arithmetic of Moduli Spaces of Coverings (2008)" and "Geometry and Arithmetic around Galois Theory (2009)". The volume focuses on geometric methods in Galois theory. The choice of the editors is to provide a complete and comprehensive account of modern points of view on Galois theory and related moduli problems, using stacks, gerbes and groupoids. It contains lecture notes on étale fundamental group and fundamental group scheme, and moduli stacks of curves and covers. Research articles complete the collection.
Book Synopsis Arithmetic Fundamental Groups and Noncommutative Algebra by : Michael D. Fried
Download or read book Arithmetic Fundamental Groups and Noncommutative Algebra written by Michael D. Fried and published by American Mathematical Soc.. This book was released on 2002 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: The arithmetic and geometry of moduli spaces and their fundamental groups are a very active research area. This book offers a complete overview of developments made over the last decade. The papers in this volume examine the geometry of moduli spaces of curves with a function on them. The main players in Part 1 are the absolute Galois group $G {\mathbb Q $ of the algebraic numbers and its close relatives. By analyzing how $G {\mathbb Q $ acts on fundamental groups defined by Hurwitz moduli problems, the authors achieve a grand generalization of Serre's program from the 1960s. Papers in Part 2 apply $\theta$-functions and configuration spaces to the study of fundamental groups over positive characteristic fields. In this section, several authors use Grothendieck's famous lifting results to give extensions to wildly ramified covers. Properties of the fundamental groups have brought collaborations between geometers and group theorists. Several Part 3 papers investigate new versions of the genus 0 problem. In particular, this includes results severely limiting possible monodromy groups of sphere covers. Finally, Part 4 papers treat Deligne's theory of Tannakian categories and arithmetic versions of the Kodaira-Spencer map. This volume is geared toward graduate students and research mathematicians interested in arithmetic algebraic geometry.
Book Synopsis Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields by : Lisa Berger
Download or read book Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields written by Lisa Berger and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study the Jacobian $J$ of the smooth projective curve $C$ of genus $r-1$ with affine model $y^r = x^r-1(x + 1)(x + t)$ over the function field $mathbb F_p(t)$, when $p$ is prime and $rge 2$ is an integer prime to $p$. When $q$ is a power of $p$ and $d$ is a positive integer, the authors compute the $L$-function of $J$ over $mathbb F_q(t^1/d)$ and show that the Birch and Swinnerton-Dyer conjecture holds for $J$ over $mathbb F_q(t^1/d)$.
Book Synopsis Rigid Geometry of Curves and Their Jacobians by : Werner Lütkebohmert
Download or read book Rigid Geometry of Curves and Their Jacobians written by Werner Lütkebohmert and published by Springer. This book was released on 2016-01-26 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents some of the most important aspects of rigid geometry, namely its applications to the study of smooth algebraic curves, of their Jacobians, and of abelian varieties - all of them defined over a complete non-archimedean valued field. The text starts with a survey of the foundation of rigid geometry, and then focuses on a detailed treatment of the applications. In the case of curves with split rational reduction there is a complete analogue to the fascinating theory of Riemann surfaces. In the case of proper smooth group varieties the uniformization and the construction of abelian varieties are treated in detail. Rigid geometry was established by John Tate and was enriched by a formal algebraic approach launched by Michel Raynaud. It has proved as a means to illustrate the geometric ideas behind the abstract methods of formal algebraic geometry as used by Mumford and Faltings. This book should be of great use to students wishing to enter this field, as well as those already working in it.
Book Synopsis Algebraic Geometry and Arithmetic Curves by : Qing Liu
Download or read book Algebraic Geometry and Arithmetic Curves written by Qing Liu and published by Oxford University Press. This book was released on 2006-06-29 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the funadmental theorem of stable reduction of Deligne-Mumford. The book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are therefore few, and the book should suit a graduate student. It contains many examples and nearly 600 exercises.
Book Synopsis The Arithmetic of Fundamental Groups by : Jakob Stix
Download or read book The Arithmetic of Fundamental Groups written by Jakob Stix and published by Springer Science & Business Media. This book was released on 2012-01-10 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the more than 100 years since the fundamental group was first introduced by Henri Poincaré it has evolved to play an important role in different areas of mathematics. Originally conceived as part of algebraic topology, this essential concept and its analogies have found numerous applications in mathematics that are still being investigated today, and which are explored in this volume, the result of a meeting at Heidelberg University that brought together mathematicians who use or study fundamental groups in their work with an eye towards applications in arithmetic. The book acknowledges the varied incarnations of the fundamental group: pro-finite, l-adic, p-adic, pro-algebraic and motivic. It explores a wealth of topics that range from anabelian geometry (in particular the section conjecture), the l-adic polylogarithm, gonality questions of modular curves, vector bundles in connection with monodromy, and relative pro-algebraic completions, to a motivic version of Minhyong Kim's non-abelian Chabauty method and p-adic integration after Coleman. The editor has also included the abstracts of all the talks given at the Heidelberg meeting, as well as the notes on Coleman integration and on Grothendieck's fundamental group with a view towards anabelian geometry taken from a series of introductory lectures given by Amnon Besser and Tamás Szamuely, respectively.
Book Synopsis Galois Groups and Fundamental Groups by : Leila Schneps
Download or read book Galois Groups and Fundamental Groups written by Leila Schneps and published by Cambridge University Press. This book was released on 2003-07-21 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: Table of contents
Book Synopsis Galois Groups and Fundamental Groups by : Tamás Szamuely
Download or read book Galois Groups and Fundamental Groups written by Tamás Szamuely and published by Cambridge University Press. This book was released on 2009-07-16 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.
Book Synopsis Win-- Women in Numbers by : Alina Carmen Cojocaru
Download or read book Win-- Women in Numbers written by Alina Carmen Cojocaru and published by American Mathematical Soc.. This book was released on 2011-01-01 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of papers on number theory which evolved out of the workshop WIN - Women in Numbers, held November 2nd-7th, 2008, in Alberta, Canada. The book includes articles showcasing outcomes from collaborative research initiated during the workshop.
Book Synopsis Algebraic Curves over a Finite Field by : J. W. P. Hirschfeld
Download or read book Algebraic Curves over a Finite Field written by J. W. P. Hirschfeld and published by Princeton University Press. This book was released on 2013-03-25 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stöhr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students.
Book Synopsis Snowbird Lectures in Algebraic Geometry by : Ravi Vakil
Download or read book Snowbird Lectures in Algebraic Geometry written by Ravi Vakil and published by American Mathematical Soc.. This book was released on 2005 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: A significant part of the 2004 Summer Research Conference on Algebraic Geometry (Snowbird, UT) was devoted to lectures introducing the participants, in particular, graduate students and recent Ph.D.'s, to a wide swathe of algebraic geometry and giving them a working familiarity with exciting, rapidly developing parts of the field. One of the main goals of the organizers was to allow the participants to broaden their horizons beyond the narrow area in which they are working. A fine selection of topics and a noteworthy list of contributors made the resulting collection of articles a useful resource for everyone interested in getting acquainted with the modern topic of algebraic geometry. The book consists of ten articles covering, among others, the following topics: the minimal model program, derived categories of sheaves on algebraic varieties, Kobayashi hyperbolicity, groupoids and quotients in algebraic geometry, rigid analytic varieties, and equivariant cohomology. Suitable for independent study, this unique volume is intended for graduate students and researchers interested in algebraic geometry.
Book Synopsis Rigid Analytic Geometry and Its Applications by : Jean Fresnel
Download or read book Rigid Analytic Geometry and Its Applications written by Jean Fresnel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rigid (analytic) spaces were invented to describe degenerations, reductions, and moduli of algebraic curves and abelian varieties. This work, a revised and greatly expanded new English edition of an earlier French text by the same authors, presents important new developments and applications of the theory of rigid analytic spaces to abelian varieties, "points of rigid spaces," étale cohomology, Drinfeld modular curves, and Monsky-Washnitzer cohomology. The exposition is concise, self-contained, rich in examples and exercises, and will serve as an excellent graduate-level text for the classroom or for self-study.
Book Synopsis Inverse Galois Theory by : Gunter Malle
Download or read book Inverse Galois Theory written by Gunter Malle and published by Springer. This book was released on 2018-07-27 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: A consistent and near complete survey of the important progress made in the field over the last few years, with the main emphasis on the rigidity method and its applications. Among others, this monograph presents the most successful existence theorems known and construction methods for Galois extensions as well as solutions for embedding problems combined with a collection of the existing Galois realizations.
Book Synopsis Fundamental Algebraic Geometry by : Barbara Fantechi
Download or read book Fundamental Algebraic Geometry written by Barbara Fantechi and published by American Mathematical Soc.. This book was released on 2005 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an outline of Alexander Grothendieck's theories. This book discusses four main themes - descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. It is suitable for those working in algebraic geometry.
Book Synopsis Abelian Varieties and Number Theory by : Moshe Jarden
Download or read book Abelian Varieties and Number Theory written by Moshe Jarden and published by American Mathematical Soc.. This book was released on 2021-05-03 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of articles on Abelian varieties and number theory dedicated to Gerhard Frey's 75th birthday. It contains original articles by experts in the area of arithmetic and algebraic geometry. The articles cover topics on Abelian varieties and finitely generated Galois groups, ranks of Abelian varieties and Mordell-Lang conjecture, Tate-Shafarevich group and isogeny volcanoes, endomorphisms of superelliptic Jacobians, obstructions to local-global principles over semi-global fields, Drinfeld modular varieties, representations of etale fundamental groups and specialization of algebraic cycles, Deuring's theory of constant reductions, etc. The book will be a valuable resource to graduate students and experts working on Abelian varieties and related areas.
Book Synopsis Kac-Moody Groups, their Flag Varieties and Representation Theory by : Shrawan Kumar
Download or read book Kac-Moody Groups, their Flag Varieties and Representation Theory written by Shrawan Kumar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kac-Moody Lie algebras 9 were introduced in the mid-1960s independently by V. Kac and R. Moody, generalizing the finite-dimensional semisimple Lie alge bras which we refer to as the finite case. The theory has undergone tremendous developments in various directions and connections with diverse areas abound, including mathematical physics, so much so that this theory has become a stan dard tool in mathematics. A detailed treatment of the Lie algebra aspect of the theory can be found in V. Kac's book [Kac-90l This self-contained work treats the algebro-geometric and the topological aspects of Kac-Moody theory from scratch. The emphasis is on the study of the Kac-Moody groups 9 and their flag varieties XY, including their detailed construction, and their applications to the representation theory of g. In the finite case, 9 is nothing but a semisimple Y simply-connected algebraic group and X is the flag variety 9 /Py for a parabolic subgroup p y C g.
