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arXiv · 1511.06131

Beilinson-Kato and Beilinson-Flach elements, Coleman-Rubin-Stark classes, Heegner points and the Perrin-Riou Conjecture

Kazim Büyükboduk
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Abstract

Our first goal in this note is to explain that a weak form of Perrin-Riou's conjecture on the non-triviality of Beilinson-Kato classes follows as an easy consequence of the Iwasawa main conjectures, and deduce its refined versions in the supersingular case from this fact and a variety of Gross-Zagier formulae. Our second goal is to set up a conceptual framework in the context of $\Lambda$-adic Kolyvagin systems to treat analogues of Perrin-Riou's conjectures for higher motives of higher rank. We apply this general discussion in order to establish a link between Heegner points on a general class of CM abelian varieties and the (conjectural) Coleman-Rubin-Stark elements we introduce here. This is a higher dimensional version of Rubin's results on rational points on CM elliptic curves.

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Kazim Büyükboduk. 2015-11-19. Beilinson-Kato and Beilinson-Flach elements, Coleman-Rubin-Stark classes, Heegner points and the Perrin-Riou Conjecture. https://arxiv.org/abs/1511.06131

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