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P Adic Hodge Theory
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Book Synopsis p-adic Hodge Theory by : Bhargav Bhatt
Download or read book p-adic Hodge Theory written by Bhargav Bhatt and published by Springer Nature. This book was released on 2020-06-15 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume contains articles related to the research presented at the 2017 Simons Symposium on p-adic Hodge theory. This symposium was focused on recent developments in p-adic Hodge theory, especially those concerning integral questions and their connections to notions in algebraic topology. This volume features original research articles as well as articles that contain new research and survey some of these recent developments. It is the first of three volumes dedicated to p-adic Hodge theory.
Book Synopsis Berkeley Lectures on P-adic Geometry by : Peter Scholze
Download or read book Berkeley Lectures on P-adic Geometry written by Peter Scholze and published by Princeton University Press. This book was released on 2020-05-26 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry. In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of p-adic geometry. Building on his discovery of perfectoid spaces, Scholze introduced the concept of “diamonds,” which are to perfectoid spaces what algebraic spaces are to schemes. The introduction of diamonds, along with the development of a mixed-characteristic shtuka, set the stage for a critical advance in the discipline. In this book, Peter Scholze and Jared Weinstein show that the moduli space of mixed-characteristic shtukas is a diamond, raising the possibility of using the cohomology of such spaces to attack the Langlands conjectures for a reductive group over a p-adic field. This book follows the informal style of the original Berkeley lectures, with one chapter per lecture. It explores p-adic and perfectoid spaces before laying out the newer theory of shtukas and their moduli spaces. Points of contact with other threads of the subject, including p-divisible groups, p-adic Hodge theory, and Rapoport-Zink spaces, are thoroughly explained. Berkeley Lectures on p-adic Geometry will be a useful resource for students and scholars working in arithmetic geometry and number theory.
Book Synopsis EXCURSION INTO P-ADIC HODGE THEORY by :
Download or read book EXCURSION INTO P-ADIC HODGE THEORY written by and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Foundations of $p$-adic Teichmuller Theory by : Shinichi Mochizuki
Download or read book Foundations of $p$-adic Teichmuller Theory written by Shinichi Mochizuki and published by American Mathematical Soc.. This book was released on 2014-01-06 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book lays the foundation for a theory of uniformization of p-adic hyperbolic curves and their moduli. On one hand, this theory generalizes the Fuchsian and Bers uniformizations of complex hyperbolic curves and their moduli to nonarchimedian places. That is why in this book, the theory is referred to as p-adic Teichmüller theory, for short. On the other hand, the theory may be regarded as a fairly precise hyperbolic analog of the Serre-Tate theory of ordinary abelian varieties and their moduli. The theory of uniformization of p-adic hyperbolic curves and their moduli was initiated in a previous work by Mochizuki. And in some sense, this book is a continuation and generalization of that work. This book aims to bridge the gap between the approach presented and the classical uniformization of a hyperbolic Riemann surface that is studied in undergraduate complex analysis. Features: Presents a systematic treatment of the moduli space of curves from the point of view of p-adic Galois representations.Treats the analog of Serre-Tate theory for hyperbolic curves.Develops a p-adic analog of Fuchsian and Bers uniformization theories.Gives a systematic treatment of a "nonabelian example" of p-adic Hodge theory. Titles in this series are co-published with International Press of Boston, Inc., Cambridge, MA.
Book Synopsis p-adic Hodge Theory, Singular Varieties, and Non-Abelian Aspects by : Bhargav Bhatt
Download or read book p-adic Hodge Theory, Singular Varieties, and Non-Abelian Aspects written by Bhargav Bhatt and published by Springer Nature. This book was released on 2023-03-28 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume contains articles related to the research presented at the 2019 Simons Symposium on p-adic Hodge theory. This symposium was focused on recent developments in p-adic Hodge theory, especially those concerning non-abelian aspects This volume contains both original research articles as well as articles that contain both new research as well as survey some of these recent developments.
Book Synopsis Towards Non-Abelian P-adic Hodge Theory in the Good Reduction Case by : Martin C. Olsson
Download or read book Towards Non-Abelian P-adic Hodge Theory in the Good Reduction Case written by Martin C. Olsson and published by American Mathematical Soc.. This book was released on 2011-02-07 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author develops a non-abelian version of $p$-adic Hodge Theory for varieties (possibly open with ``nice compactification'') with good reduction. This theory yields in particular a comparison between smooth $p$-adic sheaves and $F$-isocrystals on the level of certain Tannakian categories, $p$-adic Hodge theory for relative Malcev completions of fundamental groups and their Lie algebras, and gives information about the action of Galois on fundamental groups.
Book Synopsis p-adic Differential Equations by : Kiran S. Kedlaya
Download or read book p-adic Differential Equations written by Kiran S. Kedlaya and published by Cambridge University Press. This book was released on 2010-06-10 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers. Exercises are included at the end of each chapter to help the reader review the material, and the author also provides detailed references to the literature to aid further study.
Book Synopsis P-adic Heights and P-adic Hodge Theory by : Denis Benois
Download or read book P-adic Heights and P-adic Hodge Theory written by Denis Benois and published by . This book was released on 2020 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Abelian l-Adic Representations and Elliptic Curves by : Jean-Pierre Serre
Download or read book Abelian l-Adic Representations and Elliptic Curves written by Jean-Pierre Serre and published by CRC Press. This book was released on 1997-11-15 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one
Book Synopsis Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169) by : Kazuya Kato
Download or read book Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169) written by Kazuya Kato and published by Princeton University Press. This book was released on 2008-12-14 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1970, Phillip Griffiths envisioned that points at infinity could be added to the classifying space D of polarized Hodge structures. In this book, Kazuya Kato and Sampei Usui realize this dream by creating a logarithmic Hodge theory. They use the logarithmic structures begun by Fontaine-Illusie to revive nilpotent orbits as a logarithmic Hodge structure. The book focuses on two principal topics. First, Kato and Usui construct the fine moduli space of polarized logarithmic Hodge structures with additional structures. Even for a Hermitian symmetric domain D, the present theory is a refinement of the toroidal compactifications by Mumford et al. For general D, fine moduli spaces may have slits caused by Griffiths transversality at the boundary and be no longer locally compact. Second, Kato and Usui construct eight enlargements of D and describe their relations by a fundamental diagram, where four of these enlargements live in the Hodge theoretic area and the other four live in the algebra-group theoretic area. These two areas are connected by a continuous map given by the SL(2)-orbit theorem of Cattani-Kaplan-Schmid. This diagram is used for the construction in the first topic.
Download or read book Almost Ring Theory written by Ofer Gabber and published by Springer Science & Business Media. This book was released on 2003 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Relative p-adic hodge theory by : Kiran Sridhara Kedlaya
Download or read book Relative p-adic hodge theory written by Kiran Sridhara Kedlaya and published by . This book was released on 2015 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The p-adic Simpson Correspondence (AM-193) by : Ahmed Abbes
Download or read book The p-adic Simpson Correspondence (AM-193) written by Ahmed Abbes and published by Princeton University Press. This book was released on 2016-02-09 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: The p-adic Simpson correspondence, recently initiated by Gerd Faltings, aims at describing all p-adic representations of the fundamental group of a proper smooth variety over a p-adic field in terms of linear algebra—namely Higgs bundles. This book undertakes a systematic development of the theory following two new approaches, one by Ahmed Abbes and Michel Gros, the other by Takeshi Tsuji. The authors mainly focus on generalized representations of the fundamental group that are p-adically close to the trivial representation. The first approach relies on a new family of period rings built from the torsor of deformations of the variety over a universal p-adic thickening defined by J. M. Fontaine. The second approach introduces a crystalline-type topos and replaces the notion of Higgs bundles with that of Higgs isocrystals. The authors show the compatibility of the two constructions and the compatibility of the correspondence with the natural cohomologies. The last part of the volume contains results of wider interest in p-adic Hodge theory. The reader will find a concise introduction to Faltings' theory of almost étale extensions and a chapter devoted to the Faltings topos. Though this topos is the general framework for Faltings' approach in p-adic Hodge theory, it remains relatively unexplored. The authors present a new approach based on a generalization of P. Deligne's covanishing topos.
Book Synopsis Hodge Theory and Complex Algebraic Geometry I: by : Claire Voisin
Download or read book Hodge Theory and Complex Algebraic Geometry I: written by Claire Voisin and published by Cambridge University Press. This book was released on 2007-12-20 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a modern introduction to Kaehlerian geometry and Hodge structure. Coverage begins with variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory (with the latter being treated in a more theoretical way than is usual in geometry). The book culminates with the Hodge decomposition theorem. In between, the author proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The second part of the book investigates the meaning of these results in several directions.
Book Synopsis Introduction to Hodge Theory by : José Bertin
Download or read book Introduction to Hodge Theory written by José Bertin and published by American Mathematical Soc.. This book was released on 2002 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hodge theory originated as an application of harmonic theory to the study of the geometry of compact complex manifolds. The ideas have proved to be quite powerful, leading to fundamentally important results throughout algebraic geometry. This book consists of expositions of various aspects of modern Hodge theory. Its purpose is to provide the nonexpert reader with a precise idea of the current status of the subject. The three chapters develop distinct but closely related subjects:$L2$ Hodge theory and vanishing theorems; Frobenius and Hodge degeneration; variations of Hodge structures and mirror symmetry. The techniques employed cover a wide range of methods borrowed from the heart of mathematics: elliptic PDE theory, complex differential geometry, algebraic geometry incharacteristic $p$, cohomological and sheaf-theoretic methods, deformation theory of complex varieties, Calabi-Yau manifolds, singularity theory, etc. A special effort has been made to approach the various themes from their most na The reader should have some familiarity with differential and algebraic geometry, with other prerequisites varying by chapter. The book is suitable as an accompaniment to a second course in algebraic geometry.
Book Synopsis Relative P-adic Hodge Theory by : Kiran Sridhara Kedlaya
Download or read book Relative P-adic Hodge Theory written by Kiran Sridhara Kedlaya and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors describe a new approach to relative $p$-adic Hodge theory based on systematic use of Witt vector constructions and nonarchimedean analytic geometry in the style of both Berkovich and Huber. They give a thorough development of $\varphi$-modules over a relative Robba ring associated to a perfect Banach ring of characteristic $p$, including the relationship between these objects and etale ${\mathbb Z}_p$-local systems and ${\mathbb Q}_p$-local systems on the algebraic and analytic spaces associated to the base ring, and the relationship between (pro-)etale cohomology and $\varphi$-cohomology. They also make a critical link to mixed characteristic by exhibiting an equivalence of tensor categories between the finite etale algebras over an arbitrary perfect Banach algebra over a nontrivially normed complete field of characteristic $p$ and the finite etale algebras over a corresponding Banach ${\mathbb Q}_p$-algebra. This recovers the homeomorphism between the absolute Galois groups of ${\mathbb F}_{p}((\pi))$ and ${\mathbb Q}_{p}(\mu_{p}\infty)$ given by the field of norms construction of Fontaine and Wintenberger, as well as generalizations considered by Andreatta, Brinon, Faltings, Gabber, Ramero, Scholl, and, most recently, Scholze. Using Huber's formalism of adic spaces and Scholze's formalism of perfectoid spaces, the authors globalize the constructions to give several descriptions of the etale local systems on analytic spaces over $p$-adic fields. One of these descriptions uses a relative version of the Fargues-Fontaine curve.
Book Synopsis The p-adic Simpson Correspondence and Hodge-Tate Local Systems by : Ahmed Abbes
Download or read book The p-adic Simpson Correspondence and Hodge-Tate Local Systems written by Ahmed Abbes and published by Springer. This book was released on 2024-06-06 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book delves into the p-adic Simpson correspondence, its construction, and development. Offering fresh and innovative perspectives on this important topic in algebraic geometry, the text serves a dual purpose: it describes an important tool in p-adic Hodge theory, which has recently attracted significant interest, and also provides a comprehensive resource for researchers. Unique among the books in the existing literature in this field, it combines theoretical advances, novel constructions, and connections to Hodge-Tate local systems. This exposition builds upon the foundation laid by Faltings, the collaborative efforts of the two authors with T. Tsuji, and contributions from other researchers. Faltings initiated in 2005 a p-adic analogue of the (complex) Simpson correspondence, whose construction has been taken up in several different ways. Following the approach they initiated with T. Tsuji, the authors develop new features of the p-adic Simpson correspondence, inspired by their construction of the relative Hodge-Tate spectral sequence. First, they address the connection to Hodge-Tate local systems. Then they establish the functoriality of the p-adic Simpson correspondence by proper direct image. Along the way, they expand the scope of their original construction. The book targets a specialist audience interested in the intricate world of p-adic Hodge theory and its applications, algebraic geometry and related areas. Graduate students can use it as a reference or for in-depth study. Mathematicians exploring connections between complex and p-adic geometry will also find it valuable.
