Mod-p Poincaré duality in p-adic analytic geometry
Abstract/Contents
- Abstract
- We review the theory of almost coherent modules that was introduced in "Almost Ring Theory" by Gabber and Ramero. Then we globalize it by developing a new theory of almost coherent sheaves on schemes and on a class of "nice" formal schemes. We show that these sheaves satisfy many properties similar to usual coherent sheaves, i.e. the Almost Proper Mapping Theorem, the Formal GAGA, etc. We also construct an almost version of the Grothendieck twisted image functor f^! and verify its properties. We then study sheaves of p-adic nearby cycles on admissible formal models of rigid spaces and show that these sheaves provide examples of almost coherent sheaves. This gives a new proof of the finiteness result for ́etale cohomology of proper rigid spaces obtained before in the work of Peter Scholze "p-adic Hodge Theory For Rigid-Analytic Varities". Finally, we use these results to prove the Poincare Duality Theorem for F_p-etale cohomology groups of a smooth proper rigid space over a p-adic field K. It positively answers the question raised by P. Scholze. We also show versions of Poincare Duality for Z/p^nZ, Z_p, an Q_p-coefficients.
Description
| Type of resource | text |
|---|---|
| Form | electronic resource; remote; computer; online resource |
| Extent | 1 online resource. |
| Place | California |
| Place | [Stanford, California] |
| Publisher | [Stanford University] |
| Copyright date | 2021; ©2021 |
| Publication date | 2021; 2021 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Author | Zavyalov, Bogdan |
|---|---|
| Degree supervisor | Conrad, Brian, 1970- |
| Thesis advisor | Conrad, Brian, 1970- |
| Thesis advisor | Taylor, Richard |
| Thesis advisor | Vakil, Ravi |
| Degree committee member | Taylor, Richard |
| Degree committee member | Vakil, Ravi |
| Associated with | Stanford University, Department of Mathematics |
Subjects
| Genre | Theses |
|---|---|
| Genre | Text |
Bibliographic information
| Statement of responsibility | Bogdan Zavyalov. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis Ph.D. Stanford University 2021. |
| Location | https://purl.stanford.edu/dk927ph9825 |
Access conditions
- Copyright
- © 2021 by Bogdan Zavyalov
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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