The p-adic Simpson correspondence and Hodge-Tate local systems
Preface -- An overview -- Preliminaries -- Local Study -- Global Study -- Relative cohomologies of Higgs-Tate algebras.Local Study -- Relative cohomology of Dolbeault modules -- References -- Index.
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Sprache: | English |
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Cham, Switzerland
Springer
[2024]
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Schriftenreihe: | Lecture notes in mathematics
Volume 2345 |
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035 | |a (OCoLC)1438934487 | ||
035 | |a (DE-599)BVBBV049745862 | ||
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041 | 0 | |a eng | |
044 | |a sz |c XA-CH | ||
049 | |a DE-188 |a DE-83 | ||
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100 | 1 | |a Abbes, Ahmed |d 1970- |0 (DE-588)1090806434 |4 aut | |
245 | 1 | 0 | |a The p-adic Simpson correspondence and Hodge-Tate local systems |c Ahmed Abbes ; Michel Gros |
264 | 1 | |a Cham, Switzerland |b Springer |c [2024] | |
264 | 4 | |c © 2024 | |
300 | |a x, 443 Seiten | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
490 | 1 | |a Lecture notes in mathematics |v Volume 2345 | |
520 | 3 | |a Preface -- An overview -- Preliminaries -- Local Study -- Global Study -- Relative cohomologies of Higgs-Tate algebras.Local Study -- Relative cohomology of Dolbeault modules -- References -- Index. | |
520 | 3 | |a 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. . | |
650 | 4 | |a Geometry, Algebraic | |
650 | 4 | |a Group theory | |
650 | 4 | |a p-adic groups | |
653 | 0 | |a Algebraic geometry | |
700 | 1 | |a Gros, Michel |d 1956- |0 (DE-588)1090896387 |4 aut | |
776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-031-55914-3 |
830 | 0 | |a Lecture notes in mathematics |v Volume 2345 |w (DE-604)BV000676446 |9 2345 | |
943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-035087673 |
Datensatz im Suchindex
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---|---|
any_adam_object | |
author | Abbes, Ahmed 1970- Gros, Michel 1956- |
author_GND | (DE-588)1090806434 (DE-588)1090896387 |
author_facet | Abbes, Ahmed 1970- Gros, Michel 1956- |
author_role | aut aut |
author_sort | Abbes, Ahmed 1970- |
author_variant | a a aa m g mg |
building | Verbundindex |
bvnumber | BV049745862 |
classification_rvk | SI 850 SK 300 |
ctrlnum | (OCoLC)1438934487 (DE-599)BVBBV049745862 |
dewey-full | 512/.2 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 512 - Algebra |
dewey-raw | 512/.2 |
dewey-search | 512/.2 |
dewey-sort | 3512 12 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik |
format | Book |
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id | DE-604.BV049745862 |
illustrated | Not Illustrated |
indexdate | 2024-12-24T10:16:19Z |
institution | BVB |
isbn | 9783031559136 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035087673 |
oclc_num | 1438934487 |
open_access_boolean | |
owner | DE-188 DE-83 |
owner_facet | DE-188 DE-83 |
physical | x, 443 Seiten |
publishDate | 2024 |
publishDateSearch | 2024 |
publishDateSort | 2024 |
publisher | Springer |
record_format | marc |
series | Lecture notes in mathematics |
series2 | Lecture notes in mathematics |
spelling | Abbes, Ahmed 1970- (DE-588)1090806434 aut The p-adic Simpson correspondence and Hodge-Tate local systems Ahmed Abbes ; Michel Gros Cham, Switzerland Springer [2024] © 2024 x, 443 Seiten txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics Volume 2345 Preface -- An overview -- Preliminaries -- Local Study -- Global Study -- Relative cohomologies of Higgs-Tate algebras.Local Study -- Relative cohomology of Dolbeault modules -- References -- Index. 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. . Geometry, Algebraic Group theory p-adic groups Algebraic geometry Gros, Michel 1956- (DE-588)1090896387 aut Erscheint auch als Online-Ausgabe 978-3-031-55914-3 Lecture notes in mathematics Volume 2345 (DE-604)BV000676446 2345 |
spellingShingle | Abbes, Ahmed 1970- Gros, Michel 1956- The p-adic Simpson correspondence and Hodge-Tate local systems Lecture notes in mathematics Geometry, Algebraic Group theory p-adic groups |
title | The p-adic Simpson correspondence and Hodge-Tate local systems |
title_auth | The p-adic Simpson correspondence and Hodge-Tate local systems |
title_exact_search | The p-adic Simpson correspondence and Hodge-Tate local systems |
title_full | The p-adic Simpson correspondence and Hodge-Tate local systems Ahmed Abbes ; Michel Gros |
title_fullStr | The p-adic Simpson correspondence and Hodge-Tate local systems Ahmed Abbes ; Michel Gros |
title_full_unstemmed | The p-adic Simpson correspondence and Hodge-Tate local systems Ahmed Abbes ; Michel Gros |
title_short | The p-adic Simpson correspondence and Hodge-Tate local systems |
title_sort | the p adic simpson correspondence and hodge tate local systems |
topic | Geometry, Algebraic Group theory p-adic groups |
topic_facet | Geometry, Algebraic Group theory p-adic groups |
volume_link | (DE-604)BV000676446 |
work_keys_str_mv | AT abbesahmed thepadicsimpsoncorrespondenceandhodgetatelocalsystems AT grosmichel thepadicsimpsoncorrespondenceandhodgetatelocalsystems |