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arXiv · 1902.06523

Geometric local epsilon factors

Quentin Guignard
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Abstract

Inspired by the work of Laumon on $\varepsilon$-factors and by Deligne's $1974$ letter to Serre, we give an explicit cohomological definition of $\varepsilon$-factors for $\ell$-adic Galois representations over henselian discrete valuation fields of positive equicharacteristic $p \neq \ell$, with (not necessarily finite) perfect residue fields. These geometric local $\varepsilon$-factors are completely characterized by an explicit list of purely local properties, such as an induction formula and the compatibility with geometric class field theory in rank $1$, and satisfy a product formula for $\ell$-adic sheaves on a curve over a perfect field of characteristic $p$.

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Quentin Guignard. 2019-02-18. Geometric local epsilon factors. https://arxiv.org/abs/1902.06523

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