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arXiv · 1303.4335

A refined Beilinson-Bloch conjecture for motives of modular forms

Matteo Longo·Stefano Vigni
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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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Matteo Longo, Stefano Vigni. 2013-03-18. A refined Beilinson-Bloch conjecture for motives of modular forms. https://arxiv.org/abs/1303.4335

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