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arXiv · 1711.03196

Families of Picard modular forms and an application to the Bloch-Kato conjecture

Valentin Hernandez
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Abstract

In this article we construct a $p$-adic three dimensional Eigenvariety for the group $U(2,1)(E)$, where $E$ is a quadratic imaginary field and $p$ is inert in $E$. The Eigenvariety parametrizes Hecke eigensystems on the space of overconvergent, locally analytic, cuspidal Picard modular forms of finite slope. The method generalized the one developed in Andreatta-Iovita-Pilloni by interpolating the coherent automorphic sheaves when the ordinary locus is empty. As an application of this construction, we reprove a particular case of the Bloch-Kato conjecture for some Galois characters of $E$, extending the result of Bellaiche-Chenevier to the case of a positive sign.

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Valentin Hernandez. 2019-03-15. Families of Picard modular forms and an application to the Bloch-Kato conjecture. https://doi.org/10.1112/s0010437x1900736x

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