A refined Beilinson-Bloch conjecture for motives of modular forms
Number Theory
2013-03-19 v1 Algebraic Geometry
Abstract
We propose a refined version of the Beilinson-Bloch conjecture for the motive associated with a modular form of even weight. This conjecture relates the dimension of the image of the relevant p-adic Abel-Jacobi map to certain combinations of Heegner cycles on Kuga-Sato varieties. We prove theorems in the direction of the conjecture and, in doing so, obtain higher weight analogues of results for elliptic curves due to Darmon.
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Cite
@article{arxiv.1303.4335,
title = {A refined Beilinson-Bloch conjecture for motives of modular forms},
author = {Matteo Longo and Stefano Vigni},
journal= {arXiv preprint arXiv:1303.4335},
year = {2013}
}
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34 pages