THE JACQUET–LANGLANDS CORRESPONDENCE AND THE ARITHMETIC RIEMANN–ROCH THEOREM FOR POINTED CURVES
From MaRDI portal
Publication:3116586
DOI10.1142/S1793042112500017zbMath1237.14032arXiv0710.3374MaRDI QIDQ3116586
Publication date: 24 February 2012
Published in: International Journal of Number Theory (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0710.3374
automorphic formsArakelov geometrySelberg zeta functionJacquet-Langlands correspondencearithmetic Riemann-Roch
Arithmetic aspects of modular and Shimura varieties (11G18) Automorphic forms, one variable (11F12) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)
Related Items
Shimura curves and the abc conjecture ⋮ Twisted Hilbert modular surfaces, arithmetic intersections and the Jacquet-Langlands correspondence ⋮ The arithmetic Riemann-Roch theorem and the Jacquet-Langlands correspondence
Cites Work
- Characteristic classes for algebraic vector bundles with Hermitian metric. II
- Characteristic classes for algebraic vector bundles with Hermitian metric. I
- Determinants of Laplacians on surfaces of finite volume
- Arithmetic intersection theory
- Modular curves and the Eisenstein ideal
- Non-optimal levels of \(\text{mod }l\) modular representations
- Integral models of certain Shimura curves
- The cuspidal class number formula for the modular curves \(X_ 0(M)\) with \(M\) square-free
- Conjectures on the logarithmic derivatives of Artin \(L\)-functions at negative integers
- On modular representations of \(\text{Gal}(\overline{\mathbb Q}/\mathbb Q)\) arising from modular forms
- An arithmetic Riemann-Roch theorem
- On maps between modular Jacobians and Jacobians of Shimura curves
- Integrality of a ratio of Petersson norms and level-lowering congruences
- Automorphic forms on GL (2)
- On some results of Atkin and Lehner
- Erratum: Determinants of Laplacians on surfaces of finite volume
- COHOMOLOGICAL ARITHMETIC CHOW RINGS
- Arithmetic Moduli of Elliptic Curves. (AM-108)
- Automorphic Forms on Adele Groups. (AM-83)
- Potential theory and Lefschetz theorems for arithmetic surfaces
- Hauteur de Faltings de quotients de J o( N ), discriminants d'algebres de Hecke et congruences entre formes modulaires
- ARITHMETIC MODULI OF GENERALIZED ELLIPTIC CURVES
