Overconvergent cohomology and quaternionic Darmon points

DOI10.1112/jlms/jdu036zbMath1306.11051arXiv1307.2556OpenAlexW3103315994WikidataQ57090046 ScholiaQ57090046MaRDI QIDQ2922849

Marc Masdeu, Xavier Guitart

Publication date: 15 October 2014

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.2556

zbMATH Keywords

algorithmcohomologyelliptic curveBruhat-Tits treeHecke algebraefficient computationHeegner pointStark-Heegner point\(p\)-adic Darmon pointintegration pairing

Mathematics Subject Classification ID

Computer solution of Diophantine equations (11Y50) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)

Related Items (10)

Plectic \(p\)-adic invariants ⋮ Eichler-Shimura isomorphism and group cohomology on arithmetic groups ⋮ Darmon points on elliptic curves over number fields of arbitrary signature ⋮ Unnamed Item ⋮ Uniformization of modular elliptic curves via \(p\)-adic periods ⋮ Diagonal restrictions of \(p\)-adic Eisenstein families ⋮ Parabolic eigenvarieties via overconvergent cohomology ⋮ Rationality of Darmon points over genus fields of non-maximal orders ⋮ Stark–Heegner cycles attached to Bianchi modular forms ⋮ A quaternionic construction of \(p\)-adic singular moduli

Uses Software

• Magma
• SageMath

Cites Work

• Unnamed Item
• Unnamed Item
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• Computing systems of Hecke eigenvalues associated to Hilbert modular forms
• A Construction of Rigid Analytic Cohomology Classes for Congruence Subgroups of SL₃(ℤ)
• Elliptic Curves and Class Fields of Real Quadratic Fields: Algorithms and Evidence
• Elementary matrix decomposition and the computation of Darmon points with higher conductor
• Integration on \({\mathcal H_p}\times\mathcal H\) and arithmetic applications.

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