p-Adic Hodge theory for Artin stacks

By:

Kubrak, Dmitry

Contributor(s):

Prikhodko, Artem [Co-author]

Series: Memoirs of the American Mathematical Society ; Vol. 304; No. 1528Publication details: Providence, Rhode Island: American Mathematical Society (AMS), 2024Description: 174 p.: pbk.: 27 cmISBN:

9781470471361

ISSN:

0065-9266 (Print)
1947-6221 (Online)

Subject(s):

DDC classification:

512.74 KUB

Summary: 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. https://bookstore.ams.org/view?ProductCode=MEMO/304/1528

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Barcode
Books	IIT Gandhinagar	General	512.74 KUB (Browse shelf(Opens below))	1	Available	035844

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.

https://bookstore.ams.org/view?ProductCode=MEMO/304/1528

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