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On the infinite fern of Galois representations of unitary type

Gaëtan Chenevier (2011)

Annales scientifiques de l'École Normale Supérieure

Let E be a CM number field, p an odd prime totally split in  E , and let  X be the p -adic analytic space parameterizing the isomorphism classes of  3 -dimensional semisimple p -adic representations of  Gal ( E ¯ / E ) satisfying a selfduality condition “of type U ( 3 ) ”. We study an analogue of the infinite fern of Gouvêa-Mazur in this context and show that each irreducible component of the Zariski-closure of the modular points in  X has dimension at least 3 [ E : ] . As important steps, and in any rank, we prove that any first order...

Ordinary p -adic Eisenstein series and p -adic L -functions for unitary groups

Ming-Lun Hsieh (2011)

Annales de l’institut Fourier

The purpose of this work is to carry out the first step in our four-step program towards the main conjecture for GL 2 × 𝒦 × by the method of Eisenstein congruence on G U ( 3 , 1 ) , where 𝒦 is an imaginary quadratic field. We construct a p -adic family of ordinary Eisenstein series on the group of unitary similitudes G U ( 3 , 1 ) with the optimal constant term which is basically the product of the Kubota-Leopodlt p -adic L -function and a p -adic L -function for GL 2 × 𝒦 × . This construction also provides a different point of view of p -adic...

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