A refined Beilinson–Bloch conjecture for motives of modular forms

Longo, Matteo; Vigni, Stefano

doi:10.1090/tran/6947

A refined Beilinson–Bloch conjecture for motives of modular forms
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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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