Cycle caractéristique sur une puissance symétrique d'une courbe et déterminant de la cohomologie étale

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 étale sheaf on a curve. This generalizes a result of Gérard 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).

arXiv commentin French language. v2:Shortly after the submission on arXiv, Will Sawin kindly informed us that he had obtained in arXiv:1907.08098 a more general formula for the characteristic cycle than the one which we obtained (independently) in this text