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p-adic hodge theory for Artin stacks / Dmitry Kubrak, Artem Prikhodko

By: Contributor(s): Resource type: Ressourcentyp: BuchBookLanguage: English Series: American Mathematical Society. Memoirs of the American Mathematical Society ; volume 304, number 1528 (December 2024)Publisher: Providence, RI : American Mathematical Society, December 2024Description: v, 174 SeitenISBN:
  • 9781470471361
Subject(s): Additional physical formats: No title | Erscheint auch als: p-adic hodge theory for Artin stacks. Online-Ausgabe Providence, RI : American Mathematical Society, 2024. 1 Online-Ressource (v, 174 Seiten)MSC: MSC: 14-02 | 14A20 | 14F20 | 14F30 | 14F40 | 14F10 | 57T10 | 20G05 | 14F08 | 14L30RVK: RVK: SI 130Summary: This work is devoted to the study of integral p-adic Hodge theory in the context of Artin stacks. For a Hodge-proper stack, using the formalism of prismatic cohomology, we establish a version of p-adic Hodge theory with the étale cohomology of the Raynaud generic fiber as an input. In particular, we show that the corresponding Galois representation is crystalline and that the associated Breuil-Kisin module is given by the prismatic cohomology. An interesting new feature of the stacky setting is that the natural map between étale cohomology of the algebraic and the Raynaud generic fibers is often an equivalence even outside of the proper case. In particular, we show that this holds for global quotients [X/G] where X is a smooth proper scheme and G is a reductive group. As applications we deduce Totaro’s conjectural inequality and also set up a theory of Ainf-characteristic classes.PPN: PPN: 1916010997
Holdings
Item type Home library Shelving location Call number Status
Institutsbestand Fachbibliothek Mathematik Bibliothek / frei aufgestellt Z 57 c-304.2024,1528 Nicht ausleihbar
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