Article
Local convolution of l-adic sheaves on the torus
Author/s | Rojas León, Antonio |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2013-08 |
Deposit Date | 2016-06-08 |
Published in |
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Abstract | 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 ... 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. |
Project ID. | P08-FQM-03894
MTM2010-19298 |
Citation | Rojas León, A. (2013). Local convolution of l-adic sheaves on the torus. Mathematische Zeitschrift, 274 (3), 1211-1230. |
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