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Stark–Heegner cycles attached to Bianchi modular forms.
- 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