Cohomology of fiber systems and Mordell-Weil groups of abelian varieties
Given a real semisimple Lie group \(G\) with an arithmetic subgroup \(\Gamma\) and a representation of \(G\) in a symplectic vector space \(V\), one obtains a fiber system of abelian varieties over \(\Delta =D/\Gamma\), where \(D\) is the Hermitian symmetric domain associated to \(G\). The generic fiber being denoted by \(A\), it is shown that the Mordell-Weil group \(A(\mathbb C(\Delta))\) is finite if \(H^0(\Gamma,V)\) and \(H^1(\Gamma,V)\) are trivial.
scientific article; zbMATH DE number 4051788
scientific article