Local convolution of l-adic sheaves on the torus
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 convolu...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/42023 |
| Acceso en línea: | http://hdl.handle.net/11441/42023 https://doi.org/10.1007/s00209-012-1113-x |
| Access Level: | acceso abierto |
| Palabra clave: | Convolution ℓ-adic cohomology Monodromy Perverse sheaves |
| Sumario: | 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. |
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