An explicit bound for finite Selmer groups of adjoint type
(Un exposé de Kazuhiro Fujiwara au séminaire de théorie
des nombres de Chevaleret le 1er juillet 2002)
Résumé :
Selmer groups of Galois representations play an important role in
number
theory.
It is a generalization of ideal class groups, and the celebrated conjecture
of Bloch and Kato predicts a relation with mysterious L-values. In
the
talk, I will consider the F_p -version of the Selmer group of the adjoint
representation of an 2-dimensional representation, and try to give
the
exact dimension in terms of other basic invariants. It is related to
deformation theory of Galois representations and the tangent space
calculations.