Shuji Saito: Purity of reciprocity sheaves and theory of motives with modulus

Coffee : 14:30-15:00

Abstract: We extend Voevodsky's theory of homotopy invariant sheaves with transfer to its generalizations, reciprocity sheaves and cube-invariant sheaves introduced in joint works with Bruno Kahn and Takao Yamazaki. Assuming the base feld has characteristic zero (or admits resolution of singularities), we deduce the "homotopy t-structure" on the triangulated category of motives with modulus constructed by Kahn-Saito-Yamazaki and a formula describing its morphisms groups in terms of Nisnevich hypercohomology groups of Suslin complexes with modulus. In particular, Chow groups of zero-cycles with modulus studied by Kerz-Saito is realized as such morphisms groups.