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arXiv · 1405.3079

Rankin-Selberg Euler systems and p-adic interpolation

Guido Kings·David Loeffler·Sarah Livia Zerbes
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Abstract

We construct motivic cohomology classes attached to Rankin--Selberg convolutions of modular forms of weights $\ge 2$, show that these vary analytically in p-adic families, and relate their image under the p-adic regulator map to values of L-functions. As consequences, we prove new cases of Perrin-Riou's conjecture on motivic L-values; we prove finiteness results for Tate--Shafarevich groups for twists of elliptic curves by dihedral Artin characters; and we prove one inclusion in the Iwasawa main conjecture for a single modular form over an imaginary quadratic field.

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Guido Kings, David Loeffler, Sarah Livia Zerbes. 2014-05-13. Rankin-Selberg Euler systems and p-adic interpolation. https://arxiv.org/abs/1405.3079

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