Reciprocity sheaves

Bruno Kahn (1) , Shuji Saito (2) , Takao Yamazaki (3) , Kay Rülling (4)

1 IMJ - Institut de Mathématiques de Jussieu
2 Graduate School of Mathematics
3 Institute of Mathematics
4 Universität Duisburg-Essen = University of Duisburg-Essen [Essen]

We start developing a notion of reciprocity sheaves, generalizing Voevodsky's homotopy invariant presheaves with transfers which were used in the construction of his triangulated categories of motives. We hope reciprocity sheaves will eventually lead to the definition of a larger triangulated category of motivic nature, encompassing non homotopy invariant phenomena.

Domaines: Géométrie algébrique [math.AG]

Bruno Kahn, Shuji Saito, Takao Yamazaki, Kay Rülling. Reciprocity sheaves. Compositio Mathematica, 2016, 152 (9), pp.1851-1898. ⟨10.1112/S0010437X16007466⟩. ⟨hal-02740597⟩