The rationality of Stark-Heegner cycles attached to Bianchi modular forms -- The base-change scenario
Number Theory
2023-06-22 v4
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.
Keywords
Cite
@article{arxiv.2112.07402,
title = {The rationality of Stark-Heegner cycles attached to Bianchi modular forms -- The base-change scenario},
author = {Guhan Venkat},
journal= {arXiv preprint arXiv:2112.07402},
year = {2023}
}
Comments
52 pages. Section 4 and Appendix A expanded. Changes in Sections 5 & 6. Comments welcome!