Geodesic
Regulator Indecomposable Cycles on a Product of Elliptic Curves
Canadian mathematical bulletin, Tome 56 (2013) no. 3, pp. 640-646

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2012-017-x
Mots-clés : 14C25, real regulator, regulator indecomposable, higher Chow group, indecomposable cycle 
Türkmen, İnan Utku. Regulator Indecomposable Cycles on a Product of Elliptic Curves. Canadian mathematical bulletin, Tome 56 (2013) no. 3, pp. 640-646. doi: 10.4153/CMB-2012-017-x
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[1] [1] Bloch, S., Algebraic cycles and higher K-theory. Adv. in Math. 61 (1986), no. 3, 267–304. Google Scholar | DOI

[2] [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. Google Scholar | DOI

[3] [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] [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] [5] Lewis, J. D., A note on indecomposable motivic cohomology classes. J. Reine Angew. Math. 485 (1997), 161–172. Google Scholar | DOI

[6] [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. Google Scholar | DOI

[7] [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] [8] Spiess, M., On indecomposable elements of K1 of a product of elliptic curves. K-Theory 17 (1999), no. 4, 363–383. Google Scholar | DOI

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