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

Jean-Baptiste Teyssier (1)

1 Freie Universität Berlin

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.

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

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