Rank--two Euler systems for symmetric squares

Abstract

Let $p\ge 7$ be a prime number and $f$ a normalized eigen-newform with good reduction at $p$ such that its $p$-th Fourier coefficient vanishes. We construct a rank-two Euler system attached to the $p$-adic realization of the symmetric square motive of $f$. Furthermore, we show that the non-triviality is guaranteed by the non-vanishing of the leading term of the relevant $L$-value and the non-vanishing of a certain $p$-adic period modulo $p$.

Some of the proofs and definitions have been expanded. Some minor imprecisions have also been corrected

References in corpus (1)

• Tamagawa numbers of some crystalline representations

Cited by in corpus (3)

• A higher rank Euler system for the multiplicative group over a totally real field
• Dirichlet $L$-series at $s=0$ and the scarcity of Euler systems
• Iwasawa theory of twists of elliptic modular forms over imaginary quadratic fields at inert primes