Relative P Adic Hodge Theory
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Relative P Adic Hodge Theory
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Author : Kiran Sridhara Kedlaya
language : fr
Publisher:
Release Date : 2015
Relative P Adic Hodge Theory written by Kiran Sridhara Kedlaya and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
P Adic Hodge Theory
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Author : Bhargav Bhatt
language : en
Publisher: Springer Nature
Release Date : 2020-06-15
P Adic Hodge Theory written by Bhargav Bhatt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-15 with Mathematics categories.
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.
Towards Non Abelian P Adic Hodge Theory In The Good Reduction Case
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Author : Martin C. Olsson
language : en
Publisher: American Mathematical Soc.
Release Date : 2011-02-07
Towards Non Abelian P Adic Hodge Theory In The Good Reduction Case written by Martin C. Olsson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-07 with Mathematics categories.
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.
P Adic Hodge Theory Singular Varieties And Non Abelian Aspects
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Author : Bhargav Bhatt
language : en
Publisher: Springer Nature
Release Date : 2023-03-28
P Adic Hodge Theory Singular Varieties And Non Abelian Aspects written by Bhargav Bhatt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-28 with Mathematics categories.
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.
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Author :
language : en
Publisher: World Scientific
Release Date :
written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
The P Adic Simpson Correspondence And Hodge Tate Local Systems
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Author : Ahmed Abbes
language : en
Publisher: Springer
Release Date : 2024-06-06
The P Adic Simpson Correspondence And Hodge Tate Local Systems written by Ahmed Abbes and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-06 with Mathematics categories.
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.
Geometric And Representation Theoretic Aspects Of P Adic Motives
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Author : Xin Tong
language : en
Publisher:
Release Date : 2021
Geometric And Representation Theoretic Aspects Of P Adic Motives written by Xin Tong and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.
In this dissertation, we discuss mainly the corresponding geometric and representation theoretic aspects of relative p-adic Hodge theory and p-adic motives. To be more precise, we study the corresponding analytic geometry of the corresponding spaces over and attached to period rings in the relative p-adic Hodge theory, including derived topological de Rham complexes and derived topological logarithmic de Rham complexes after Bhatt, Gabber, Guo and Illusie which is in some sense equivalent to the derived prismatic cohomology of Bhatt-Scholze as shown in the work of Li-Liu, OB[subscript]dR-sheaves after Scholze, [phi]-C̃[subscript]x-sheaves and relative-B-pairs after Kedlaya-Liu, multidimensional rings after Carter-Kedlaya-Zábrádi and Pal-Zábrádi and many other possible general universal motivic rings or sheaves. Many contexts are expected to be sheafified, such as over Scholze's pro-étale sites of the considered analytic spaces by using perfectoids or the quasisyntomic sites by using quasiregular semiperfectoids as in the work of Bhatt-Morrow-Scholze and Bhatt-Scholze. The main motivation comes from the corresponding noncommutative Tamagawa Number conjectures after Burns-Flach-Fukaya-Kato, relative version of the generalized version of the period rings as in the work of Carter-Kedlaya-Zábrádi and Pal-Zábrádi, arithmetic families of the representations of fundamental groups in analytic geometry such as for analytification of the moduli stacks of algebraic curves after Reinecke, arithmetic families of general motivic structures in analytic geometry such as in the work of Andreatta-Brinon, Andreatta-Iovita, Berger, Bhatt-Morrow-Scholze, Bhatt-Scholze, Fargues-Fontaine, Fargues-Scholze, Fontaine and Kedlaya-Liu, noncommutative analytic geometry and noncommutative deformation, derived noncommutative analytic geometry and derived noncommutative deformation, Langlands programs, analytic approach to algebraic topology and so on. Due to the natural though not functorial correspondence between the linear topology and the one induced by a Banach norm, we do not restrict ourselves to the functional analytic point of view when we take completion after Bambozzi-Ben-Bassat-Kremnizer, Clausen-Scholze, Gabber-Ramero, Huber, Kedlaya-Liu and Scholze.
Supersingular P Adic L Functions Maass Shimura Operators And Waldspurger Formulas
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Author : Daniel Kriz
language : en
Publisher: Princeton University Press
Release Date : 2021-11-09
Supersingular P Adic L Functions Maass Shimura Operators And Waldspurger Formulas written by Daniel Kriz and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-09 with Mathematics categories.
A groundbreaking contribution to number theory that unifies classical and modern results This book develops a new theory of p-adic modular forms on modular curves, extending Katz's classical theory to the supersingular locus. The main novelty is to move to infinite level and extend coefficients to period sheaves coming from relative p-adic Hodge theory. This makes it possible to trivialize the Hodge bundle on the infinite-level modular curve by a "canonical differential" that restricts to the Katz canonical differential on the ordinary Igusa tower. Daniel Kriz defines generalized p-adic modular forms as sections of relative period sheaves transforming under the Galois group of the modular curve by weight characters. He introduces the fundamental de Rham period, measuring the position of the Hodge filtration in relative de Rham cohomology. This period can be viewed as a counterpart to Scholze's Hodge-Tate period, and the two periods satisfy a Legendre-type relation. Using these periods, Kriz constructs splittings of the Hodge filtration on the infinite-level modular curve, defining p-adic Maass-Shimura operators that act on generalized p-adic modular forms as weight-raising operators. Through analysis of the p-adic properties of these Maass-Shimura operators, he constructs new p-adic L-functions interpolating central critical Rankin-Selberg L-values, giving analogues of the p-adic L-functions of Katz, Bertolini-Darmon-Prasanna, and Liu-Zhang-Zhang for imaginary quadratic fields in which p is inert or ramified. These p-adic L-functions yield new p-adic Waldspurger formulas at special values.
P Adic Differential Equations
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Author : Kiran Kedlaya
language : en
Publisher: Cambridge University Press
Release Date : 2022-06-09
P Adic Differential Equations written by Kiran Kedlaya and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-09 with Mathematics categories.
A detailed and unified treatment of $P$-adic differential equations, from the basic principles to the current frontiers of research.
Berkeley Lectures On P Adic Geometry
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Author : Peter Scholze
language : en
Publisher: Princeton University Press
Release Date : 2020-05-26
Berkeley Lectures On P Adic Geometry written by Peter Scholze and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-26 with Mathematics categories.
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.