Nearby slopes and boundedness for $\ell$-adic sheaves in positive characteristic
Algebraic Geometry
2015-06-10 v1 Number Theory
Abstract
The goal of this paper is to motivate a boundedness conjecture on nearby slopes of -adic sheaves in positive characteristic, and to prove it for smooth curves. For a constructible -adic sheaf, we prove the finiteness of the set of nearby slopes associated to a given morphism. For the constant sheaf, we prove the vanishing of nearby slopes in case of generalized semi-stable reduction.
Keywords
Cite
@article{arxiv.1506.02849,
title = {Nearby slopes and boundedness for $\ell$-adic sheaves in positive characteristic},
author = {Jean-Baptiste Teyssier},
journal= {arXiv preprint arXiv:1506.02849},
year = {2015}
}