Geometric local ε-factors in higher dimensions

Guignard, Quentin

doi:10.1017/S1474748021000037

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Geometric local ε-factors in higher dimensions

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Guignard, Quentin
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1017/S1474748021000037
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Citation

Guignard, Q. (2022). Geometric local ε-factors in higher dimensions. Journal of the Institute of Mathematics of Jussieu, 21(6), 1887-1913. doi:10.1017/S1474748021000037.

Cite as: https://hdl.handle.net/21.11116/0000-0009-701A-C

Abstract

We prove a product formula for the determinant of the cohomology of an étale sheaf with -adic coefficients over an arbitrary proper scheme over a perfect field of positive characteristic p distinct from. The local contributions are constructed by iterating vanishing cycle functors as well as certain exact additive functors that can be considered as linearised versions of Artin conductors and local -factors. We provide several applications of our higher dimensional product formula, such as twist formulas for global -factors.