Revista Matemática Iberoamericana


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Volume 34, Issue 3, 2018, pp. 1373–1386
DOI: 10.4171/RMI/1027

Published online: 2018-08-27

Explicit local multiplicative convolution of $\ell$-adic sheaves

Antonio Rojas-León[1]

(1) Universidad de Sevilla, Spain

We give explicit formulas for the local multiplicative convolution functors, which express the local monodromies of the convolution of two $\ell$-adic sheaves on the torus $\mathbb G_m$ over the algebraic closure of a finite field in terms of the local monodromies of the factors. As a particular case, we recover Fu's formulas for the local Fourier transform.

Keywords: $/ell$-adic cohomology, convolution, Galois representations of local fields

Rojas-León Antonio: Explicit local multiplicative convolution of $\ell$-adic sheaves. Rev. Mat. Iberoamericana 34 (2018), 1373-1386. doi: 10.4171/RMI/1027