We prove that the p-adic L-series of the tensor square of a p-ordinary modular form factors as the product of the symmetric square p-adic L-series of the form and a Kubota– Leopoldt p-adic L-series. This establishes a generalization of a conjecture of Citro. Greenberg’s exceptional zero conjecture for the adjoint follows as a corollary of our theorem. Our method of proof follows that of Gross, ...

2 Derived p-adic heights 2.1 Derived heights for cyclic groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Comparison of pairings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 Compatibility of the derived heights . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4 Derived p-adic heights . . . . . . . . . . . . . . . . . . . . . . . . . ....

Some problems on algebraic groups over global fields like the congruence subgroup problem involve the determination of topological central extensions of the adelic group which, in turn, leads naturally to the study of topological central extensions of p-adic Lie groups by finite groups like the group of roots of unity in the p-adic field. Moreover, central extensions of semisimple p-adic Lie gr...

There exists an infinite family of p-compact groups whose Weyl groups correspond to the finite p-adic pseudoreflection groups G(q, r, n) of family 2a in the Clark-Ewing list. In this paper we study these p-compact groups. In particular, we construct an analog of the classical Whitney sum map, a family of monomorphisms and a spherical fibration which produces an analog of the classical J-homomor...