An anticyclotomic Euler system for adjoint modular Galois representations
Copyright policy )An anticyclotomic Euler system for adjoint modular Galois representations
Let K be an imaginary quadratic field and p a prime split in K. In this paper we construct an anticyclotomic Euler system for the adjoint representation attached to elliptic modular forms base changed to K. We also relate our Euler system to a p-adic L-function deduced from the construction by Eischen–Wan and Eischen–Harris–Li–Skinner of p-adic L-functions for unitary groups. This allows us to derive new cases of the Bloch–Kato conjecture in rank zero, and a divisibility towards an Iwasawa main conjecture.
- Grenoble Alpes University France
- University of California, Santa Barbara United States
symmetric square, Euler systems, Mathematics - Number Theory, Modular and Shimura varieties, \(p\)-adic theory, local fields, 11R23 (Primary) 11F85, 14G35 (Secondary), \(p\)-adic families of modular forms, FOS: Mathematics, Bloch-Kato conjecture, Number Theory (math.NT), Iwasawa theory, diagonal cycles
symmetric square, Euler systems, Mathematics - Number Theory, Modular and Shimura varieties, \(p\)-adic theory, local fields, 11R23 (Primary) 11F85, 14G35 (Secondary), \(p\)-adic families of modular forms, FOS: Mathematics, Bloch-Kato conjecture, Number Theory (math.NT), Iwasawa theory, diagonal cycles
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