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K-groups of reciprocity functors for and abelian varieties

Published online by Cambridge University Press:  10 October 2014

Kay Rülling  and
Takao Yamazaki
Kay Rülling
Affiliation:
Freie Universität Berlin, Arnimallee 3, 14195 Berlin, Germany, [email protected]
Takao Yamazaki
Affiliation:
Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan, [email protected]
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Abstract

We prove that the K-group of reciprocity functors, defined by F. Ivorra and the first author, vanishes over a perfect field as soon as one of the reciprocity functors is and one is an abelian variety.

Keywords

Reciprocity functorChow groupK-group19E1514F4219D4519F15
Type
Research Article
Information
Journal of K-Theory , Volume 14 , Issue 3 , December 2014 , pp. 556 - 569
Copyright
Copyright © ISOPP 2014 

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References

AK.Altman, A. and Kleiman, S., Bertini theorems for hypersurface sections containing a subscheme. Comm. Algebra 7 (1979), 775–790.Google Scholar
Ha.Hartshorne, R., Algebraic Geometry. Graduate Texts in Mathematics 52, Springer-Verlag, 1977, xvi+496.CrossRefGoogle Scholar
H.Hiranouchi, T., An additive variant of Somekawa's K-groups and Kähler differentials. J. K-Theory 13 (2014), 481–516.CrossRefGoogle Scholar
HK.Huber, A. and Kahn, B., The slice filtration and mixed Tate motives. Compositio Math. 142 (2006), 907–936.Google Scholar
IR.Ivorra, F. and Rülling, K., K-groups of reciprocity functors. Preprint 2012, http://arxiv.org/abs/1209.1217.Google Scholar
K.Kahn, B., Foncteurs de Mackey à réciprocité. Preprint, http://arxiv.org/abs/1210.7577.Google Scholar
KY.Kahn, B. and Yamazaki, T., Voevodsky's motives and Weil reciprocity, Duke Math. J. 162 (2013), 2751–2796.Google Scholar
M.Mumford, D., Abelian varieties, Tata Institute of Fundamental Research Studies in Mathematics 5, Oxford University Press, London 1970.Google Scholar
SS.Saito, S. and Sato, K., Algebraic cycles and étale cohomology (in Japanese). Maruzen (2012).Google Scholar
Se.Serre, J.-P., Algebraic groups and class fields. Graduate Texts in Mathematics 117, Springer-Verlag, 1988, x+207.Google Scholar
So.Somekawa, M., On Milnor K-groups attached to semi-abelian varieties. K-Theory 4 (1990), 105–119.Google Scholar
V.Voevodsky, V., Cohomological theory of presheaves with transfers. in Cycles, , transfers, and motivic homology theories, Ann. of Math. Stud. 143, Princeton Univ. Press, 2000, 87–137.Google Scholar
W.Weil, A., Basic number theory. 3rd ed. Die Grundlehren der Mathematischen Wissenschaften 144. Springer-Verlag, 1974.CrossRefGoogle Scholar