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Rigid Cohomology For Algebraic Stacks
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Book Synopsis Rigid Cohomology for Algebraic Stacks by : David Brown
Download or read book Rigid Cohomology for Algebraic Stacks written by David Brown and published by . This book was released on 2010 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: We extend le Stum's construction of the overconvergent site to algebraic stacks. We prove that etale morphisms are morphisms of cohomological descent for finitely presnted crystals on the overconvergent site. Finally, using the notion of an open subtopos of SGA4, we define a notion of overconvergent cohomology supported in a closed substack and show that it agrees with the classical notion of rigid cohomology supported in a closed subscheme.
Book Synopsis Crystalline Cohomology of Algebraic Stacks and Hyodo-Kato Cohomology by : Martin C. Olsson
Download or read book Crystalline Cohomology of Algebraic Stacks and Hyodo-Kato Cohomology written by Martin C. Olsson and published by . This book was released on 2007 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text the author uses stack-theoretic techniques to study the crystalline structure on the de Rham cohomology of a proper smooth scheme over a $p$-adic field and applications to $p$-adic Hodge theory. He develops a general theory of crystalline cohomology and de Rham-Witt complexes for algebraic stacks and applies it to the construction and study of the $(\varphi, N, G)$-structure on de Rham cohomology. Using the stack-theoretic point of view instead of log geometry, he develops the ingredients needed to prove the $C_{\text {st}}$-conjecture using the method of Fontaine, Messing, Hyodo, Kato, and Tsuji, except for the key computation of $p$-adic vanishing cycles. He also generalizes the construction of the monodromy operator to schemes with more general types of reduction than semistable and proves new results about tameness of the action of Galois on cohomology.
Book Synopsis Rigid Cohomology over Laurent Series Fields by : Christopher Lazda
Download or read book Rigid Cohomology over Laurent Series Fields written by Christopher Lazda and published by Springer. This book was released on 2016-04-27 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, the authors develop a new theory of p-adic cohomology for varieties over Laurent series fields in positive characteristic, based on Berthelot's theory of rigid cohomology. Many major fundamental properties of these cohomology groups are proven, such as finite dimensionality and cohomological descent, as well as interpretations in terms of Monsky-Washnitzer cohomology and Le Stum's overconvergent site. Applications of this new theory to arithmetic questions, such as l-independence and the weight monodromy conjecture, are also discussed. The construction of these cohomology groups, analogous to the Galois representations associated to varieties over local fields in mixed characteristic, fills a major gap in the study of arithmetic cohomology theories over function fields. By extending the scope of existing methods, the results presented here also serve as a first step towards a more general theory of p-adic cohomology over non-perfect ground fields. Rigid Cohomology over Laurent Series Fields will provide a useful tool for anyone interested in the arithmetic of varieties over local fields of positive characteristic. Appendices on important background material such as rigid cohomology and adic spaces make it as self-contained as possible, and an ideal starting point for graduate students looking to explore aspects of the classical theory of rigid cohomology and with an eye towards future research in the subject.
Book Synopsis Algebraic Geometry by : Dan Abramovich
Download or read book Algebraic Geometry written by Dan Abramovich and published by American Mathematical Soc.. This book was released on 2009 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers information on various technical tools, from jet schemes and derived categories to algebraic stacks. This book delves into the geometry of various moduli spaces, including those of stable curves, stable maps, coherent sheaves, and abelian varieties. It describes various advances in higher-dimensional bi rational geometry.
Book Synopsis Rigid Cohomology by : Bernard Le Stum
Download or read book Rigid Cohomology written by Bernard Le Stum and published by Cambridge University Press. This book was released on 2007-09-06 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dating back to work of Berthelot, rigid cohomology appeared as a common generalization of Monsky-Washnitzer cohomology and crystalline cohomology. It is a p-adic Weil cohomology suitable for computing Zeta and L-functions for algebraic varieties on finite fields. Moreover, it is effective, in the sense that it gives algorithms to compute the number of rational points of such varieties. This is the first book to give a complete treatment of the theory, from full discussion of all the basics to descriptions of the very latest developments. Results and proofs are included that are not available elsewhere, local computations are explained, and many worked examples are given. This accessible tract will be of interest to researchers working in arithmetic geometry, p-adic cohomology theory, and related cryptographic areas.
Book Synopsis Local Cohomology Sheaves on Algebraic Stacks by : Tobias Sitte
Download or read book Local Cohomology Sheaves on Algebraic Stacks written by Tobias Sitte and published by . This book was released on 2014 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Rigid Local Systems by : Nicholas M. Katz
Download or read book Rigid Local Systems written by Nicholas M. Katz and published by Princeton University Press. This book was released on 1996 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Riemann introduced the concept of a "local system" on P1-{a finite set of points} nearly 140 years ago. His idea was to study nth order linear differential equations by studying the rank n local systems (of local holomorphic solutions) to which they gave rise. His first application was to study the classical Gauss hypergeometric function, which he did by studying rank-two local systems on P1- {0,1,infinity}. His investigation was successful, largely because any such (irreducible) local system is rigid in the sense that it is globally determined as soon as one knows separately each of its local monodromies. It became clear that luck played a role in Riemann's success: most local systems are not rigid. Yet many classical functions are solutions of differential equations whose local systems are rigid, including both of the standard nth order generalizations of the hypergeometric function, n F n-1's, and the Pochhammer hypergeometric functions. This book is devoted to constructing all (irreducible) rigid local systems on P1-{a finite set of points} and recognizing which collections of independently given local monodromies arise as the local monodromies of irreducible rigid local systems. Although the problems addressed here go back to Riemann, and seem to be problems in complex analysis, their solutions depend essentially on a great deal of very recent arithmetic algebraic geometry, including Grothendieck's etale cohomology theory, Deligne's proof of his far-reaching generalization of the original Weil Conjectures, the theory of perverse sheaves, and Laumon's work on the l-adic Fourier Transform.
Book Synopsis Geometric Aspects of Dwork Theory by : Alan Adolphson
Download or read book Geometric Aspects of Dwork Theory written by Alan Adolphson and published by Walter de Gruyter. This book was released on 2004 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Étale Cohomology of Rigid Analytic Varieties and Adic Spaces by : Roland Huber
Download or read book Étale Cohomology of Rigid Analytic Varieties and Adic Spaces written by Roland Huber and published by Springer. This book was released on 2013-07-01 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diese Forschungsmonographie von hohem mathematischen Niveau liefert einen neuen Zugang zu den rigid-analytischen Räumen, sowie ihrer etalen Kohomologie.USP: Aus der Froschung: Zahlentheorie und Algebraische Geometrie
Book Synopsis Noncommutative Motives by : Gonçalo Tabuada
Download or read book Noncommutative Motives written by Gonçalo Tabuada and published by American Mathematical Soc.. This book was released on 2015-09-21 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of motives began in the early 1960s when Grothendieck envisioned the existence of a "universal cohomology theory of algebraic varieties". The theory of noncommutative motives is more recent. It began in the 1980s when the Moscow school (Beilinson, Bondal, Kapranov, Manin, and others) began the study of algebraic varieties via their derived categories of coherent sheaves, and continued in the 2000s when Kontsevich conjectured the existence of a "universal invariant of noncommutative algebraic varieties". This book, prefaced by Yuri I. Manin, gives a rigorous overview of some of the main advances in the theory of noncommutative motives. It is divided into three main parts. The first part, which is of independent interest, is devoted to the study of DG categories from a homotopical viewpoint. The second part, written with an emphasis on examples and applications, covers the theory of noncommutative pure motives, noncommutative standard conjectures, noncommutative motivic Galois groups, and also the relations between these notions and their commutative counterparts. The last part is devoted to the theory of noncommutative mixed motives. The rigorous formalization of this latter theory requires the language of Grothendieck derivators, which, for the reader's convenience, is revised in a brief appendix.
Download or read book Etale Cohomology Theory written by Lei Fu and published by World Scientific. This book was released on 2011-01-31 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: New Edition available hereEtale cohomology is an important branch in arithmetic geometry. This book covers the main materials in SGA 1, SGA 4, SGA 4 1/2 and SGA 5 on etale cohomology theory, which includes decent theory, etale fundamental groups, Galois cohomology, etale cohomology, derived categories, base change theorems, duality, and l-adic cohomology. The prerequisites for reading this book are basic algebraic geometry and advanced commutative algebra.
Book Synopsis Homotopical Algebraic Geometry II: Geometric Stacks and Applications by : Bertrand Toën
Download or read book Homotopical Algebraic Geometry II: Geometric Stacks and Applications written by Bertrand Toën and published by American Mathematical Soc.. This book was released on 2008 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second part of a series of papers called "HAG", devoted to developing the foundations of homotopical algebraic geometry. The authors start by defining and studying generalizations of standard notions of linear algebra in an abstract monoidal model category, such as derivations, étale and smooth morphisms, flat and projective modules, etc. They then use their theory of stacks over model categories to define a general notion of geometric stack over a base symmetric monoidal model category $C$, and prove that this notion satisfies the expected properties.
Book Synopsis Non-Archimedean Analysis by : Siegfried Bosch
Download or read book Non-Archimedean Analysis written by Siegfried Bosch and published by Springer. This book was released on 2012-06-28 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: : So eine Illrbeit witb eigentIid) nie rertig, man muli iie fur fertig erfHiren, wenn man nad) 8eit nnb Umftiinben bas moglid)fte get an qat. (@oetqe
Book Synopsis Etale Cohomology and the Weil Conjecture by : Eberhard Freitag
Download or read book Etale Cohomology and the Weil Conjecture written by Eberhard Freitag and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some years ago a conference on l-adic cohomology in Oberwolfach was held with the aim of reaching an understanding of Deligne's proof of the Weil conjec tures. For the convenience of the speakers the present authors - who were also the organisers of that meeting - prepared short notes containing the central definitions and ideas of the proofs. The unexpected interest for these notes and the various suggestions to publish them encouraged us to work somewhat more on them and fill out the gaps. Our aim was to develop the theory in as self contained and as short a manner as possible. We intended especially to provide a complete introduction to etale and l-adic cohomology theory including the monodromy theory of Lefschetz pencils. Of course, all the central ideas are due to the people who created the theory, especially Grothendieck and Deligne. The main references are the SGA-notes [64-69]. With the kind permission of Professor J. A. Dieudonne we have included in the book that finally resulted his excellent notes on the history of the Weil conjectures, as a second introduction. Our original notes were written in German. However, we finally followed the recommendation made variously to publish the book in English. We had the good fortune that Professor W. Waterhouse and his wife Betty agreed to translate our manuscript. We want to thank them very warmly for their willing involvement in such a tedious task. We are very grateful to the staff of Springer-Verlag for their careful work.
Book Synopsis An Introduction to Homological Algebra by : Charles A. Weibel
Download or read book An Introduction to Homological Algebra written by Charles A. Weibel and published by Cambridge University Press. This book was released on 1995-10-27 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: The landscape of homological algebra has evolved over the last half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and semi-simple Lie algebras are also described. This book is suitable for second or third year graduate students. The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences. Homology of group and Lie algebras illustrate these topics. Intermingled are less canonical topics, such as the derived inverse limit functor lim1, local cohomology, Galois cohomology, and affine Lie algebras. The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors. By making these tools more accessible, the book helps to break down the technological barrier between experts and casual users of homological algebra.
Book Synopsis Cohomological and Geometric Approaches to Rationality Problems by : Fedor Bogomolov
Download or read book Cohomological and Geometric Approaches to Rationality Problems written by Fedor Bogomolov and published by Springer Science & Business Media. This book was released on 2009-11-03 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rationality problems link algebra to geometry, and the difficulties involved depend on the transcendence degree of $K$ over $k$, or geometrically, on the dimension of the variety. A major success in 19th century algebraic geometry was a complete solution of the rationality problem in dimensions one and two over algebraically closed ground fields of characteristic zero. Such advances has led to many interdisciplinary applications to algebraic geometry. This comprehensive book consists of surveys of research papers by leading specialists in the field and gives indications for future research in rationality problems. Topics discussed include the rationality of quotient spaces, cohomological invariants of quasi-simple Lie type groups, rationality of the moduli space of curves, and rational points on algebraic varieties. This volume is intended for researchers, mathematicians, and graduate students interested in algebraic geometry, and specifically in rationality problems. Contributors: F. Bogomolov; T. Petrov; Y. Tschinkel; Ch. Böhning; G. Catanese; I. Cheltsov; J. Park; N. Hoffmann; S. J. Hu; M. C. Kang; L. Katzarkov; Y. Prokhorov; A. Pukhlikov
Book Synopsis Comparison of Relatively Unipotent Log de Rham Fundamental Groups by : Bruno Chiarellotto
Download or read book Comparison of Relatively Unipotent Log de Rham Fundamental Groups written by Bruno Chiarellotto and published by American Mathematical Society. This book was released on 2023-09-15 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
