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Regulator Indecomposable Cycles on a Product of Elliptic Curves

Published online by Cambridge University Press:  20 November 2018

İnan Utku Türkmen
İnan Utku Türkmen*
Affiliation:
Department of Mathematics, Bilkent University, Ankara, Turkey, 06800 e-mail: [email protected]
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Abstract.

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We provide a novel proof of the existence of regulator indecomposables in the cycle group $C{{H}^{2}}\left( X,\,1 \right)$, where $X$ is a sufficiently general product of two elliptic curves. In particular, the nature of our proof provides an illustration of Beilinson rigidity.

Keywords

14C25real regulatorregulator indecomposablehigher Chow groupindecomposable cycle
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 3 , 01 September 2013 , pp. 640 - 646
Copyright
Copyright © Canadian Mathematical Society 2013

References

[1] Bloch, S., Algebraic cycles and higher K-theory. Adv. in Math. 61 (1986), no. 3, 267–304. http://dx.doi.org/10.1016/0001-8708(86)90081-2 Google Scholar
[2] Chen, X. and Lewis, J. D., The Hodge-D-conjecture for K3 and abelian surfaces. J. Algebraic Geom. 14 (2005), no. 2, 213–240. http://dx.doi.org/10.1090/S1056-3911-04-00390-X http://dx.doi.org/10.1090/S1056-3911-04-00390-X Google Scholar
[3] Collino, A., Griffiths’ infinitesimal invariant and higher K-theory on hyperelliptic Jacobians. J. Algebraic Geom. 6 (1997), no. 3, 393–415.Google Scholar
[4] Gordon, B. B. and Lewis, J. D., Indecomposable higher Chow cycles on products of elliptic curves. J. Algebraic Geom. 8 (1999), no. 3, 543–567.Google Scholar
[5] Lewis, J. D., A note on indecomposable motivic cohomology classes. J. Reine Angew. Math. 485 (1997), 161–172. http://dx.doi.org/10.1515/crll.1997.485.161 Google Scholar
[6] Mildenhall, S. J. M., Cycles in a product of elliptic curves, and a group analogous to the class group. Duke Math. J. 67 (1992), no. 2, 387–406. http://dx.doi.org/10.1215/S0012-7094-92-06715-9 http://dx.doi.org/10.1215/S0012-7094-92-06715-9 Google Scholar
[7] Müller-Stach, S. J., Constructing indecomposable motivic cohomology classes on algebraic surfaces. J. Algebraic Geom. 6 (1997), no. 3, 513–543.Google Scholar
[8] Spiess, M., On indecomposable elements of K1 of a product of elliptic curves. K-Theory 17 (1999), no. 4, 363–383. http://dx.doi.org/10.1023/A:1007739216643 http://dx.doi.org/10.1023/A:1007739216643 Google Scholar