English

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 \ell-adic sheaves in positive characteristic, and to prove it for smooth curves. For a constructible \ell-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}
}