The p-adic Simpson Correspondence (AM-193) / / Ahmed Abbes, Takeshi Tsuji, Michel Gros.
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 f...
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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2016] ©2016 |
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Abbes, Ahmed, author. aut http://id.loc.gov/vocabulary/relators/aut The p-adic Simpson Correspondence (AM-193) / Ahmed Abbes, Takeshi Tsuji, Michel Gros. Princeton, NJ : Princeton University Press, [2016] ©2016 1 online resource (616 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 193 Frontmatter -- Contents -- Foreword -- Chapter I. Representations of the fundamental group and the torsor of deformations. An overview -- Chapter II. Representations of the fundamental group and the torsor of deformations. Local study -- Chapter III. Representations of the fundamental group and the torsor of deformations. Global aspects -- Chapter IV. Cohomology of Higgs isocrystals -- Chapter V. Almost étale coverings -- Chapter VI. Covanishing topos and generalizations -- Facsimile : A p-adic Simpson correspondence -- Bibliography -- Indexes restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Geometry, Algebraic. Group theory. p-adic groups. MATHEMATICS / Algebra / Linear. bisacsh Dolbeault generalized representation. Dolbeault module. Dolbeault representation. Faltings cohomology. Faltings extension. Faltings ringed topos. Faltings site. Faltings topos. Galois cohomology. Gerd Faltings. Higgs bundle. Higgs bundles. Higgs crystals. Higgs envelopes. Higgs isocrystal. HiggsДate algebra. HodgeДate representation. HodgeДate structure. HodgeДate theory. Hyodo's theory. Koszul complex. additive categories. adic module. almost faithfully flat descent. almost faithfully flat module. almost flat module. almost isomorphism. almost tale covering. almost tale extension. cohomology. covanishing topos. crystalline-type topos. deformation. discrete AЇ-module. finite tale site. fundamental group. generalized covanishing topos. generalized representation. inverse limit. linear algebra. locally irreducible scheme. morphism. overconvergence. p-adic Hodge theory. p-adic Simpson correspondence. p-adic field. period ring. ringed covanishing topos. ringed total topos. small generalized representation. small representation. solvable Higgs module. tale cohomology. tale fundamental group. torsor. Abbes, Ahmed, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Faltings, Gerd, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Gros, Michel, author. aut http://id.loc.gov/vocabulary/relators/aut Gros, Michel, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Tsuji, Takeshi, author. aut http://id.loc.gov/vocabulary/relators/aut Tsuji, Takeshi, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2016 9783110485103 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2016 9783110485288 ZDB-23-DMA Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2016 9783110638592 print 9780691170282 https://doi.org/10.1515/9781400881239 https://www.degruyter.com/isbn/9781400881239 Cover https://www.degruyter.com/document/cover/isbn/9781400881239/original |
language |
English |
format |
eBook |
author |
Abbes, Ahmed, Abbes, Ahmed, Gros, Michel, Tsuji, Takeshi, |
spellingShingle |
Abbes, Ahmed, Abbes, Ahmed, Gros, Michel, Tsuji, Takeshi, The p-adic Simpson Correspondence (AM-193) / Annals of Mathematics Studies ; Frontmatter -- Contents -- Foreword -- Chapter I. Representations of the fundamental group and the torsor of deformations. An overview -- Chapter II. Representations of the fundamental group and the torsor of deformations. Local study -- Chapter III. Representations of the fundamental group and the torsor of deformations. Global aspects -- Chapter IV. Cohomology of Higgs isocrystals -- Chapter V. Almost étale coverings -- Chapter VI. Covanishing topos and generalizations -- Facsimile : A p-adic Simpson correspondence -- Bibliography -- Indexes |
author_facet |
Abbes, Ahmed, Abbes, Ahmed, Gros, Michel, Tsuji, Takeshi, Abbes, Ahmed, Abbes, Ahmed, Faltings, Gerd, Faltings, Gerd, Gros, Michel, Gros, Michel, Gros, Michel, Gros, Michel, Tsuji, Takeshi, Tsuji, Takeshi, Tsuji, Takeshi, Tsuji, Takeshi, |
author_variant |
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VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
author2 |
Abbes, Ahmed, Abbes, Ahmed, Faltings, Gerd, Faltings, Gerd, Gros, Michel, Gros, Michel, Gros, Michel, Gros, Michel, Tsuji, Takeshi, Tsuji, Takeshi, Tsuji, Takeshi, Tsuji, Takeshi, |
author2_variant |
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author_sort |
Abbes, Ahmed, |
title |
The p-adic Simpson Correspondence (AM-193) / |
title_full |
The p-adic Simpson Correspondence (AM-193) / Ahmed Abbes, Takeshi Tsuji, Michel Gros. |
title_fullStr |
The p-adic Simpson Correspondence (AM-193) / Ahmed Abbes, Takeshi Tsuji, Michel Gros. |
title_full_unstemmed |
The p-adic Simpson Correspondence (AM-193) / Ahmed Abbes, Takeshi Tsuji, Michel Gros. |
title_auth |
The p-adic Simpson Correspondence (AM-193) / |
title_alt |
Frontmatter -- Contents -- Foreword -- Chapter I. Representations of the fundamental group and the torsor of deformations. An overview -- Chapter II. Representations of the fundamental group and the torsor of deformations. Local study -- Chapter III. Representations of the fundamental group and the torsor of deformations. Global aspects -- Chapter IV. Cohomology of Higgs isocrystals -- Chapter V. Almost étale coverings -- Chapter VI. Covanishing topos and generalizations -- Facsimile : A p-adic Simpson correspondence -- Bibliography -- Indexes |
title_new |
The p-adic Simpson Correspondence (AM-193) / |
title_sort |
the p-adic simpson correspondence (am-193) / |
series |
Annals of Mathematics Studies ; |
series2 |
Annals of Mathematics Studies ; |
publisher |
Princeton University Press, |
publishDate |
2016 |
physical |
1 online resource (616 p.) Issued also in print. |
contents |
Frontmatter -- Contents -- Foreword -- Chapter I. Representations of the fundamental group and the torsor of deformations. An overview -- Chapter II. Representations of the fundamental group and the torsor of deformations. Local study -- Chapter III. Representations of the fundamental group and the torsor of deformations. Global aspects -- Chapter IV. Cohomology of Higgs isocrystals -- Chapter V. Almost étale coverings -- Chapter VI. Covanishing topos and generalizations -- Facsimile : A p-adic Simpson correspondence -- Bibliography -- Indexes |
isbn |
9781400881239 9783110485103 9783110485288 9783110494914 9783110638592 9780691170282 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA179 |
callnumber-sort |
QA 3179 A23 42017 |
url |
https://doi.org/10.1515/9781400881239 https://www.degruyter.com/isbn/9781400881239 https://www.degruyter.com/document/cover/isbn/9781400881239/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
512 - Algebra |
dewey-full |
512.2 |
dewey-sort |
3512.2 |
dewey-raw |
512.2 |
dewey-search |
512.2 |
doi_str_mv |
10.1515/9781400881239 |
oclc_num |
934626614 |
work_keys_str_mv |
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ids_txt_mv |
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is_hierarchy_title |
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