Rankin-Eisenstein classes for modular forms

By G. Kings, David Loeffler, Sarah Livia Zerbes. American Journal of Mathematics, 2015

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abstract:In this paper we make a systematic study of certain motivic cohomology classes (``Rankin-Eisenstein classes'') attached to the Rankin-Selberg convolution of two modular forms of weight $\ge 2$. The main result is the computation of the $p$-adic syntomic regulators of these classes. As a consequence we prove many cases of the Perrin-Riou conjecture for Rankin-Selberg convolutions of cusp forms.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/29d6ff3da51f2768bb4bd8fcef1a4f9a002afd37