A Remark on Deligne's Finiteness Theorem

作者：Esnault Helene^*

来源：International Mathematics Research Notices, 2017, (16): 4962-4970.

DOI：10.1093/imrn/rnw157

Over a connected geometrically unibranch scheme X of finite type over a finite field, we show, with purely geometric arguments, finiteness of the number of irreducible (Q) over bar (l)-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 [7, Definition 3.6], this is Deligne's theorem [7, Theorem 1.1], the proof of which uses the whole strength of [3] and [6]. We also generalize Deligne's theorem [7, Theorem 1.1] from X smooth to X normal, using Deligne's theorem (not reproving it) and a few more geometric arguments.

• 出版日期2017-8