Crystallinity properties of complex rigid local systems [not online]
Helene Esnault (Freie Universität Berlin)
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): agstanford.com
Organizer: | Ravi Vakil* |
*contact for this listing |