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arXiv · 1506.02849

Nearby slopes and boundedness for $\ell$-adic sheaves in positive characteristic

Jean-Baptiste Teyssier
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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.

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Jean-Baptiste Teyssier. 2015-06-09. Nearby slopes and boundedness for $\ell$-adic sheaves in positive characteristic. https://arxiv.org/abs/1506.02849

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