arXiv subjects

Joël Riou

Publications and source records attributed to Joël Riou.

3 recordsLinked to original sources

arXiv2023

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

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).

math.AG↗

arXiv2012

Opérations de Steenrod motiviques

This article fills some gaps in Voevodsky's construction of the Steenrod operations acting on the motivic cohomology with coefficients in Z/lZ of motivic spaces in the sense of Morel and Voevodsky over a perfect field of characteristic different from l. Moreover, as a consequence of the method of proof of a theorem by Voevodsky on stable cohomology operations, we show that the spectrum that represents motivic cohomology with coefficients Z/lZ has no nonzero "superphantom" endomorphism.

math.AG↗

arXiv2009

Algebraic K-theory, A^1-homotopy and Riemann-Roch theorems

In this article, we show that the combination of the constructions done in SGA 6 and the A^1-homotopy theory naturally leads to results on higher algebraic K-theory. This applies to the operations on algebraic K-theory, Chern characters and Riemann-Roch theorems.

math.KT↗