Opened Access Local convolution of l-adic sheaves on the torus

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Autor: Rojas León, Antonio
Departamento: Universidad de Sevilla. Departamento de álgebra
Fecha: 2013-08
Publicado en: Mathematische Zeitschrift, 274 (3), 1211-1230.
Tipo de documento: Artículo
Resumen: For K and L two l-adic perverse sheaves on the one-dimensional torus Gm,k¯ over the algebraic closure of a finite field, we show that the local monodromies of their convolution K ∗ L at its points of non-smoothness is completely determined by the local monodromies of K and L. We define local convolution bi-exact functors ρ(u) (s,t) for every s, t, u ∈ P 1 k¯that map continuous l-adic representations of the inertia groups at s and t to a representation of the inertia group at u, and show that the local monodromy of K ∗ L at u is the direct sum of the ρ(u) (s,t) applied to the local monodromies of K and L. This generalizes a previous result of N. Katz for the case where K and L are smooth, tame at 0 and totally wild at infinity.
Cita: Rojas León, A. (2013). Local convolution of l-adic sheaves on the torus. Mathematische Zeitschrift, 274 (3), 1211-1230.
Tamaño: 393.7Kb
Formato: PDF

URI: http://hdl.handle.net/11441/42023

DOI: http://dx.doi.org/10.1007/s00209-012-1113-x

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