Reciprocity sheaves

Abstract

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.

59 pages, two appendices by Kay Rülling

References in corpus (2)

• Birational motives, II: Triangulated birational motives
• Motives with modulus

Cited by in corpus (9)

• Relative cycles with moduli and regulator maps
• Motives with modulus, III: The categories of motives
• Reciprocity sheaves and their ramification filtrations
• Gysin triangles in the category of motifs with modulus
• A motivic homotopy theory without ${\mathbb{A}}^1$ invariance
• A remark on the tensor product of SC-reciprocity sheaves
• Semi-purity for cycles with modulus
• A motivic integral $p$-adic cohomology
• Connectivity and Purity for logarithmic motives