Cohomology of algebraic varieties / Cohomologie des variétés algébriques

Collection Cohomology of algebraic varieties / Cohomologie des variétés algébriques

Organizer(s) Cadoret, Anna ; Charles, François ; Demarche, Cyril ; Klingler, Bruno ; Moonen, Ben
Date(s) 15/10/2018 - 19/10/2018
linked URL https://conferences.cirm-math.fr/1775.html
00:00:00 / 00:00:00
3 6

Relative integral $p$-adic Hodge theory

By Matthew Morrow

Given a smooth scheme $X$ over the ring of integers of a $p$-adic field, we introduce the notion of a relative Breuil-Kisin-Fargues module $M$ on $X$. Each such $M$ simultaneously encodes the data of a lisse étale sheaf, a module with flat connection, and a crystal, whose cohomologies are then intertwined by a relative form of the $A_{inf}$ cohomology introduced in "Integral $p$-adic Hodge theory" by Bhatt-M-Scholze. They are moreover closely related to other work in relative $p$-adic Hodge theory, notably Faltings small generalised representations and his relative Fontaine Lafaille theory. Joint with Takeshi Tsuji.

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Citation data

  • DOI 10.24350/CIRM.V.19466503
  • Cite this video MORROW, Matthew (18/10/2018). Relative integral $p$-adic Hodge theory. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19466503
  • URL https://dx.doi.org/10.24350/CIRM.V.19466503

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