6 citations · 12 across the 7 of their papers we have counts for
8 papers
Generalized Jacobians of graphs
Bruce W. Jordan, Kenneth A. Ribet, Anthony J. Scholl
We define a generalized Jacobian and a generalized Picard group of a graph with respect…
Modular curves and Néron models of generalized Jacobians
Bruce W. Jordan, Kenneth A. Ribet, Anthony J. Scholl
Let be a smooth geometrically connected projective curve over the field of fractions of a discrete valuation ring , and a modulus on , given by a closed su…
Linear independence in linear systems on elliptic curves
Bradley W. Brock, Bruce W. Jordan, Bjorn Poonen +2
Let be an elliptic curve, with identity , and let be a cyclic subgroup of odd order , over an algebraically closed field with . For…
Extensions in the cohomology of Hilbert modular varieties
Cosmin Davidescu, Anthony J. Scholl
We describe extension classes arising in the -adic and Hodge cohomology of Hilbert modular varieties, generalising results of Caspar to arbitrary dimensions. We show that thi…
Modular forms, de Rham cohomology and congruences
Matija Kazalicki, Anthony J. Scholl
In this paper we show that Atkin and Swinnerton-Dyer type of congruences hold for weakly modular forms (modular forms that are permitted to have poles at cusps). Unlike the case of…
Hypersurfaces and the Weil conjectures
A. J. Scholl
We give a proof that the Riemann hypothesis for hypersurfaces over finite fields implies the result for all smooth proper varieties, by a deformation argument which does not use th…