Rankin-Selberg Euler systems and p-adic interpolation

2014/05/13 by Kings, Guido, Loeffler, David, Zerbes, Sarah Livia
#11F67 #11F85 #11G40 #14G35 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1405.3079

Abstract

We construct motivic cohomology classes attached to Rankin--Selberg convolutions of modular forms of weights ≥ 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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