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• W2969500270 abstract "In this paper we develop a new method to study Iwasawa theory and Eisenstein families for unitary groups $mathrm{U}(r,s)$ of general signature over a totally real field $F$. As a consequence we prove that for a motive corresponding to a regular algebraic cuspidal automorphic representation $pi$ on $mathrm{U}(r,s)_{/F}$ which is ordinary at $p$, twisted by a Hecke character, if its Selmer group has rank $0$, then the corresponding central $L$-value is nonzero. This generalizes a result of Skinner-Urban in their ICM 2006 report in the special case when $F=mathbb{Q}$ and the motive is conjugate self-dual. Along the way we also obtain $p$-adic functional equations for the corresponding $p$-adic $L$-functions and $p$-adic families of Klingen Eisenstein series. Our method does not involve computing Fourier-Jacobi coefficients (as opposed to previous work which only work in low rank cases, e.g. $mathrm{U}(1,1)$, $mathrm{U}(2,0)$ and $mathrm{U}(1,0)$) whose automorphic interpretation is unclear in general." @default.
• W2969500270 created "2019-08-29" @default.
• W2969500270 creator A5020266094 @default.
• W2969500270 date "2019-08-20" @default.
• W2969500270 modified "2023-09-27" @default.
• W2969500270 title "Iwasawa theory for $mathrm{U}(r,s)$, Bloch-Kato conjecture and Functional Equation" @default.
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