Iwasawa theory and Bloch-Kato conjecture for unitary groups    

Xin Wan, Morningside Center of Mathematics

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We describe a new method to study Eisenstein family and Iwasawa theory on unitary groups over totally real fields of general signatures. As a consequence we prove that if the central L-value of a cuspidal eigenform on the unitary group twisted by a CM character is 0, then the corresponding Selmer group has positive rank. The method also has a byproduct the p-adic functional equations for p-adic L-functions and p-adic families of Eisenstein series on unitary groups.