K-groups of reciprocity functors

Ivorra, Florian; Rülling, Kay

doi:10.1090/jag/678

Authors: Florian Ivorra and Kay Rülling
Journal: J. Algebraic Geom. 26 (2017), 199-278
DOI: https://doi.org/10.1090/jag/678
Published electronically: September 23, 2016
MathSciNet review: 3606996
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Abstract | References | Additional Information

Abstract: In this work we introduce reciprocity functors, construct the associated K-group functor of a family of reciprocity functors, which itself is a reciprocity functor, and compute it in several different cases. It may be seen as a first attempt to get close to the notion of reciprocity sheaves imagined by B. Kahn. Commutative algebraic groups, homotopy invariant Nisnevich sheaves with transfers, cycle modules or Kähler differentials are examples of reciprocity functors. As commutative algebraic groups do, reciprocity functors are equipped with symbols and satisfy a reciprocity law for curves.

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Additional Information

Florian Ivorra
Affiliation: Institut de Recherche Mathématique de Rennes, UMR 6625 du CNRS, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes cedex, France
MR Author ID: 781701
Email: florian.ivorra@univ-rennes1.fr

Kay Rülling
Affiliation: Institut für Mathematik, Freie Universität Berlin, 14195 Berlin, Germany
Email: kay.ruelling@fu-berlin.de

Received by editor(s): January 19, 2014
Received by editor(s) in revised form: September 5, 2014
Published electronically: September 23, 2016
Additional Notes: The first author acknowledges support from the DAAD (Deutscher Akademischer Austausch Dienst) during the preparation of this work and thanks M. Levine for providing an excellent working environment and making his stay at the University Duisburg-Essen possible. The second author was supported by the SFB/TR 45 “Periods, moduli spaces and arithmetic of algebraic varieties” of the DFG, by the ERC Advanced Grant 226257, and thanks the first author for an invitation to the University of Rennes in 2010
Article copyright: © Copyright 2016 University Press, Inc.