The aim of this note is twofold. Firstly, we prove an explicit reciprocity law for certain diagonal classes in the ´etale cohomology of the triple product of a modular curve, stated in [8] and used there as a crucial ingredient in the proof of the main results. Secondly, we apply the aforementioned reciprocity law to address the rank-zero case of the equivariant Bloch–Kato conjecture for the self-dual motive of an elliptic newform of weight k > 2. In the special case k = 2, our result gives a self-contained and simpler proof of the main result of [15].
Diagonal classes and the Bloch–Kato conjecture / M. Bertolini, M.A. Seveso, R. Venerucci. - In: MÜNSTER JOURNAL OF MATHEMATICS. - ISSN 1867-5778. - 13:2(2020), pp. 317-352. [10.17879/90169661145]
Diagonal classes and the Bloch–Kato conjecture
M. Bertolini;M.A. Seveso;R. Venerucci
2020
Abstract
The aim of this note is twofold. Firstly, we prove an explicit reciprocity law for certain diagonal classes in the ´etale cohomology of the triple product of a modular curve, stated in [8] and used there as a crucial ingredient in the proof of the main results. Secondly, we apply the aforementioned reciprocity law to address the rank-zero case of the equivariant Bloch–Kato conjecture for the self-dual motive of an elliptic newform of weight k > 2. In the special case k = 2, our result gives a self-contained and simpler proof of the main result of [15].File | Dimensione | Formato | |
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