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GEOMETRIC LOCAL $\varepsilon $-FACTORS IN HIGHER DIMENSIONS

Part of: (Co)homology theory

Published online by Cambridge University Press:  02 September 2021

Quentin Guignard Open the ORCID record for Quentin Guignard [Opens in a new window]
Quentin Guignard*
Affiliation:
Max Planck Institute for Mathematics, Vivatsgasse 7, 53111Bonn, Germany ([email protected])
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Abstract

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We prove a product formula for the determinant of the cohomology of an étale sheaf with $\ell $ -adic coefficients over an arbitrary proper scheme over a perfect field of positive characteristic p distinct from $\ell $ . 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 $\varepsilon $ -factors. We provide several applications of our higher dimensional product formula, such as twist formulas for global $\varepsilon $ -factors.

Keywords

étale cohomologyε-factorsconductors

MSC classification

Primary: 14F20: Étale and other Grothendieck topologies and (co)homologies
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 21 , Issue 6 , November 2022 , pp. 1887 - 1913
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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