Nearby slopes and boundedness for ℓ-adic sheaves in positive characteristic

Abstract : The goal of this paper is to motivate a boundedness conjecture on nearby slopes of ℓ-adic sheaves in positive characteristic, and to prove it for smooth curves. For a constructible ℓ-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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https://hal.archives-ouvertes.fr/hal-01161856
Contributor : Jean-Baptiste Teyssier <>
Submitted on : Tuesday, June 9, 2015 - 11:42:54 AM
Last modification on : Wednesday, February 27, 2019 - 11:08:02 AM
Document(s) archivé(s) le : Tuesday, September 15, 2015 - 1:35:26 PM

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  • HAL Id : hal-01161856, version 1
  • ARXIV : 1506.02849

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Jean-Baptiste Teyssier. Nearby slopes and boundedness for ℓ-adic sheaves in positive characteristic. 2015. ⟨hal-01161856⟩

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