Cohomologically proper stacks over Zp̳ : algebra, geometry and representation theory
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | eng |
| Published: |
Massachusetts Institute of Technology
2020
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/1721.1/126926 |
| _version_ | 1826216386722004992 |
|---|---|
| author | Kubrak, Dmitry(Dmitrii) |
| author2 | Roman Bezrukavnikov. |
| author_facet | Roman Bezrukavnikov. Kubrak, Dmitry(Dmitrii) |
| author_sort | Kubrak, Dmitry(Dmitrii) |
| collection | MIT |
| description | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020 |
| first_indexed | 2024-09-23T16:46:50Z |
| format | Thesis |
| id | mit-1721.1/126926 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T16:46:50Z |
| publishDate | 2020 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1269262020-09-04T03:01:35Z Cohomologically proper stacks over Zp̳ : algebra, geometry and representation theory Kubrak, Dmitry(Dmitrii) Roman Bezrukavnikov. Massachusetts Institute of Technology. Department of Mathematics. Massachusetts Institute of Technology. Department of Mathematics Mathematics. Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020 Cataloged from the official PDF of thesis. In title on title page, double underscored "p" appears as subscript. Includes bibliographical references (pages 291-297). Abstract In this thesis, we study a class of so-called cohomologically proper stacks from various perspectives, mainly concentrating on the p-adic context. Cohomological properness is a relaxed properness condition on a stack which roughly asks the cohomology of any coherent sheaf to be finitely generated over the base. We extend some of the techniques available for smooth proper schemes to smooth cohomologically proper stacks, featuring in particular recently developed theory of prismatic co-homology and the classical Deligne-Illusie method for the Hodge-to-de Rham degeneration. As main applications we prove the Totaro's conjectural inequality between the dimensions of the de Rham and the singular F[subscript p]-cohomology of the classifying stack of a reductive group, compute the ring of prismatic characteristic classes at non-torsion primes and give some new examples of the Hodge-to-de Rham degeneration for stacks in characteristic 0. We also study some descent properties of certain Brauer group classes on conical resolutions, a question having some applications to the theory of Fedosov quantizations in characteristic p. Some surprising results about the G[subscript m]-weights of differential 1-forms that are obtained along the way, originally motivated the attempt to generalize the integral p-adic Hodge theory to the setting of cohomologically proper stacks. by Dmitry Kubrak. Ph. D. Ph.D. Massachusetts Institute of Technology, Department of Mathematics 2020-09-03T16:41:02Z 2020-09-03T16:41:02Z 2020 2020 Thesis https://hdl.handle.net/1721.1/126926 1191266925 eng MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided. http://dspace.mit.edu/handle/1721.1/7582 297 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Kubrak, Dmitry(Dmitrii) Cohomologically proper stacks over Zp̳ : algebra, geometry and representation theory |
| title | Cohomologically proper stacks over Zp̳ : algebra, geometry and representation theory |
| title_full | Cohomologically proper stacks over Zp̳ : algebra, geometry and representation theory |
| title_fullStr | Cohomologically proper stacks over Zp̳ : algebra, geometry and representation theory |
| title_full_unstemmed | Cohomologically proper stacks over Zp̳ : algebra, geometry and representation theory |
| title_short | Cohomologically proper stacks over Zp̳ : algebra, geometry and representation theory |
| title_sort | cohomologically proper stacks over zp algebra geometry and representation theory |
| topic | Mathematics. |
| url | https://hdl.handle.net/1721.1/126926 |
| work_keys_str_mv | AT kubrakdmitrydmitrii cohomologicallyproperstacksoverzpalgebrageometryandrepresentationtheory |