Ashutosh Roy Choudhury

Artin vanishing along the $\ell$-adic tower of an abelian variety

Let $A$ be an abelian variety of dimension $g$ over an algebraically closed field and let $\ell$ be a prime invertible in the field. For every constructible $\mathbb{F}_{\ell}$-sheaf $F$ on $A$ we prove that there is an integer $e$, depending on $F$, such that the pullback map $[\ell^{e}]^{*}\colon\mathrm{H}^{i}(A,[\el...