The rationality of Stark-Heegner cycles attached to Bianchi modular forms -- The base-change scenario

Abstract

We study Stark-Heegner cycles attached to Bianchi modular forms, that is automorphic forms for GL(2) over an imaginary quadratic field F . The Stark-Heegner cycles are local cohomology classes in the p-adic Galois representation associated to the Bianchi eigenform. They are conjectured to be the restriction (at a prime p) of global cohomology classes in the (semistable) Bloch-Kato Selmer group defined over ring class fields of a relative quadratic extension K/F. In this paper, we show that these conjectures hold when the Bianchi eigenform is the base-change of a classical elliptic cuspform.