11 citations · 22 across the 11 of their papers we have counts for
11 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…
Another look at rational torsion of modular Jacobians
Kenneth A. Ribet, Preston Wake
We study the rational torsion subgroup of the modular Jacobian for a square-free integer. We give a new proof of a result of Ohta on a generalization of Ogg's conjectu…
Robert F. Coleman 1954-2014
Matthew Baker, Barry Mazur, Ken Ribet
Robert F. Coleman, a highly original mathematician who has had a profound influence on modern number theory and arithmetic geometry, passed away on March 24, 2014. We give an overv…
Modular forms with large coefficient fields via congruences
Luis Dieulefait, Jorge Jimenez Urroz, Kenneth Ribet
In this paper we apply results from the theory of congruences of modular forms (control of reducible primes, level-lowering), the modularity of elliptic curves and Q-curves, and a…
Torsion points on modular curves and Galois theory
Kenneth A. Ribet, Minhyong Kim
We outline the proof of a theorem of M. Baker and A. Tamagawa that gives a complete description of the torsion points on a modular curve embedded in its Jacobian using the notion o…