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Stark–Heegner cycles attached to Bianchi modular forms.

Authors :
Venkat, Guhan
Williams, Chris
Source :
Journal of the London Mathematical Society. Jul2021, Vol. 104 Issue 1, p394-422. 29p.
Publication Year :
2021

Abstract

Let f be a Bianchi modular form, that is, an automorphic form for GL(2) over an imaginary quadratic field F, and let p be a prime of F at which f is new. Let K be a quadratic extension of F, and L(f/K,s) the L‐function of the base‐change of f to K. Under certain hypotheses on f and K, the functional equation of L(f/K,s) ensures that it vanishes at the central point. The Bloch–Kato conjecture predicts that this should force the existence of non‐trivial classes in an appropriate global Selmer group attached to f and K. In this paper, we use the theory of double integrals developed by Salazar and the second author to construct certain p‐adic Abel–Jacobi maps, which we use to propose a construction of such classes via Stark–Heegner cycles. This builds on ideas of Darmon and in particular generalises an approach of Rotger and Seveso in the setting of classical modular forms. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00246107
Volume :
104
Issue :
1
Database :
Academic Search Index
Journal :
Journal of the London Mathematical Society
Publication Type :
Academic Journal
Accession number :
151432333
Full Text :
https://doi.org/10.1112/jlms.12438