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Reciprocity sheaves

Part of: $K$-theory in geometry $K$-theory in number theory Higher algebraic $K$-theory (Co)homology theory

Published online by Cambridge University Press:  14 July 2016

Bruno Kahn ,
Shuji Saito ,
Takao Yamazaki  and
Kay Rülling
Bruno Kahn
Affiliation:
IMJ-PRG, Case 247, 4 place Jussieu, 75252 Paris Cedex 05, France email bruno.kahn@imj-prg.fr
Shuji Saito
Affiliation:
Interactive Research Center of Science, Graduate School of Science and Engineering, Tokyo Institute of Technology, 2-12-1 Okayama, Meguro, Tokyo 152-8551, Japan email sshuji@msb.biglobe.ne.jp
Takao Yamazaki
Affiliation:
Institute of Mathematics, Tohoku University, Aoba, Sendai 980-8578, Japan email ytakao@math.tohoku.ac.jp
Kay Rülling
Affiliation:
Freie Universität Berlin, Arnimallee 7, 14195 Berlin, Germany email kay.ruelling@fu-berlin.de
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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 that reciprocity sheaves will eventually lead to the definition of larger triangulated categories of motivic nature, encompassing non-homotopy invariant phenomena.

Keywords

presheaves with transfershomotopy invarianceWeil reciprocity

MSC classification

Primary: 19E15: Algebraic cycles and motivic cohomology
Secondary: 14F42: Motivic cohomology; motivic homotopy theory 19D45: Higher symbols, Milnor $K$-theory 19F15: Symbols and arithmetic

Information

Type
Research Article
Information
Compositio Mathematica , Volume 152 , Issue 9 , September 2016 , pp. 1851 - 1898
Copyright
© The Authors 2016 

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