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Let $X$ be a smooth connected projective algebraic curve over an algebraically closed field, and let $S$ be a finite nonempty closed subset in $X$. We study deformations of $overline{mathbb F}_ell$-sheaves. The universal deformation space is a formal scheme. Its generic fiber has a rigid analytic space structure. By studying this rigid analytic space, we prove a conjecture of Katz which says that if a lisse $overline{mathbb Q}_ell$-sheaf $mathcal F$ on $X-S$ is irreducible and rigid, then we have $mathrm{dim}, H^1(X,j_astmathcal End(mathcal F))=2g$, where $j:X-Sto X$ is the open immersion, and $g$ is the genus of $X$.
Tautological systems was introduced in Lian-Yau as the system of differential equations satisfied by period integrals of hyperplane sections of some complex projective homogenous varieties. We introduce the $ell$-adic tautological systems for the case where the ground field is of characteristic $p$.
We lift the classical Hasse--Weil zeta function of varieties over a finite field to a map of spectra with domain the Grothendieck spectrum of varieties constructed by Campbell and Zakharevich. We use this map to prove that the Grothendieck spectrum o
For a complex connected semisimple linear algebraic group G of adjoint type and of rank n, De Concini and Procesi constructed its wonderful compactification bar{G}, which is a smooth Fano G times G-variety of Picard number n enjoying many interesting
We construct a functor from the category of p-adic etale local systems on a smooth rigid analytic variety X over a p-adic field to the category of vector bundles with an integrable connection over its base change to B_dR, which can be regarded as a f
We study the moduli space of rank 2 instanton sheaves on $p3$ in terms of representations of a quiver consisting of 3 vertices and 4 arrows between two pairs of vertices. Aiming at an alternative compactification for the moduli space of instanton she