Reciprocity sheaves

Bruno Kahn; Shuji Saito; Takao Yamazaki; Kay Rülling

doi:10.1112/S0010437X16007466

Reciprocity sheaves

Bruno Kahn, Shuji Saito, Takao Yamazaki, Kay Rülling

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1851-1898
Number of pages	48
Journal	Compositio Mathematica
Volume	152
Issue number	9
DOIs	https://doi.org/10.1112/S0010437X16007466
Publication status	Published - 2016 Sep 1

Keywords

Weil reciprocity
homotopy invariance
presheaves with transfers

ASJC Scopus subject areas

Algebra and Number Theory

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10.1112/S0010437X16007466

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title = "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 that reciprocity sheaves will eventually lead to the definition of larger triangulated categories of motivic nature, encompassing non-homotopy invariant phenomena.",

keywords = "Weil reciprocity, homotopy invariance, presheaves with transfers",

author = "Bruno Kahn and Shuji Saito and Takao Yamazaki and Kay R{\"u}lling",

note = "Funding Information: The first author acknowledges the support of Agence Nationale de la Recherche (ANR) under reference ANR-12-BL01-0005. The second author is supported by JSPS KAKENHI Grant 22340003. The third author is supported by JSPS KAKENHI Grants 22684001 and 24654001. Publisher Copyright: {\textcopyright} The Authors 2016.",

year = "2016",

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doi = "10.1112/S0010437X16007466",

language = "English",

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TY - JOUR

T1 - Reciprocity sheaves

AU - Kahn, Bruno

AU - Saito, Shuji

AU - Yamazaki, Takao

AU - Rülling, Kay

N1 - Funding Information: The first author acknowledges the support of Agence Nationale de la Recherche (ANR) under reference ANR-12-BL01-0005. The second author is supported by JSPS KAKENHI Grant 22340003. The third author is supported by JSPS KAKENHI Grants 22684001 and 24654001. Publisher Copyright: © The Authors 2016.

PY - 2016/9/1

Y1 - 2016/9/1

N2 - 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.

AB - 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.

KW - Weil reciprocity

KW - homotopy invariance

KW - presheaves with transfers

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JO - Compositio Mathematica

JF - Compositio Mathematica

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IS - 9

ER -

Reciprocity sheaves

Abstract

Keywords

ASJC Scopus subject areas

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