Crystallinity properties of complex rigid local systems [not online]

Helene Esnault (Freie Universit├Ąt Berlin)

28-Apr-2023, 19:00-20:00 (14 months ago)

Abstract: Joint work in progress with Michael Groechenig

We prove in all generality that on a smooth complex quasi-projective variety $X$, Rigid connections yield $F$-isocrystals on almost all good reductions $X_{\mathbb F_q}$ and that rigid local systems yield crystalline local systems on $X_K$ for $K$ the field of fractions of the Witt vectors of a finite field $\mathbb F_q$, for almost all $X_{\mathbb F_q}$. This improves our earlier work where, if $X$ was not projective, we assumed a strong cohomological condition (which is fulfilled for Shimura varieties of real rank $\geq 2$), and we obtained only infinitely many $\mathbb F_q$ of growing characteristic. While the earlier proof was via characteristic $p$, the new one is purely $p$-adic and uses $p$-adic topology.

We shall discuss the projective case during the lecture.

algebraic geometry

Audience: researchers in the topic

Stanford algebraic geometry seminar

Series comments: The seminar was online for a significant period of time, but for now is solely in person. More seminar information (including slides and videos, when available):

Organizer: Ravi Vakil*
*contact for this listing

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