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arXiv · 2312.07776

Cycle caract\'eristique sur une puissance sym\'etrique d'une courbe et d\'eterminant de la cohomologie \'etale

Fabrice Orgogozo·Joël Riou
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Abstract

Relying on the formalism developed by Alexander Beilinson and Takeshi Saito, we compute the characteristic cycle of an external symmetric power of a tame \'etale sheaf on a curve. This generalizes a result of G\'erard Laumon in characteristic 0 and leads to a result of local acyclicity of the Abel-Jacobi morphism, due to Pierre Deligne and motivated by his geometric approach to the product formula for the determinant of cohomology (epsilon factor).

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Fabrice Orgogozo, Joël Riou. 2023-12-12. Cycle caract\'eristique sur une puissance sym\'etrique d'une courbe et d\'eterminant de la cohomologie \'etale. https://doi.org/10.2140/tunis.2026.8.413

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