A remark on Deligne's finiteness theorem

Hélène Esnault

Published 2016-02-29Version 1

Over a connected geometrically unibranch scheme $X$ of finite type over a finite field, we show finiteness of the number of irreducible $\bar \Q_\ell$-lisse sheaves, with bounded rank and bounded ramification in the sense of Drinfeld, up to twist by a character of the finite field. On $X$ smooth, with bounded ramification in the sense of bounding the Swan conductors on curves, this is Deligne's theorem.