Density of arithmetic representations

Abstract: The lecture surveys recent work with Moritz Kerz. The motivation is the conjecture that the Hard-Lefschetz (HL) property holds on smooth projective varieties defined over algebraically closed char. $p>0$ fields for cohomology with values in semi-simple $\ell$-adic local systems $V$. We know it is true if $V$ comes from geometry (Deligne, Beilinson-Bernstein-Deligne-Gabber) by Deligne’s theory of weights. In absence of weights, we proved it if $V$ has rank $1$ and reduced the whole HL conjecture to a density conjecture on arithmetic semi-simple $\ell$-adic systems on $P^1$ minus $3$ closed points, which we can prove in rank $2$.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

The seminar takes place on Tuesdays and Thursdays via Zoom. Zoom passwords are given via mailing list on Fridays. To join the mailing list go to the website.

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