Washington State University
Combinatorics, Linear Algebra and Number Theory (CLaN) Seminar
Department of Mathematics
Neill Hall 5W
April 20, Monday, 4:10 - 5:00 PM
Jennifer Johnson-Leung
Department of Mathematics
University of Idaho
Combinatorics, Linear Algebra and Number Theory (CLaN) Seminar
Department of Mathematics
Neill Hall 5W
April 20, Monday, 4:10 - 5:00 PM
Jennifer Johnson-Leung
Department of Mathematics
University of Idaho
Title: Modularity of Abelian Surfaces
Abstract: In 2013, Freitas, Bao V. Le Hung, and Samir Siksek released a paper proving that elliptic curves over real quadratic fields are modular. This result generalizes the celebrated theorem of Wiles, et. al., proving that elliptic curves over Q are modular. I will recall the statement of these theorems and explain how we expect them to generalize to abelian surfaces in the Paramodular Conjecture of Brumer and Kramer. The Paramodular Conjecture is known for surfaces that arise as Weil restrictions of elliptic curves over real quadratic fields by a result of Brooks Roberts and myself.
Abstract: In 2013, Freitas, Bao V. Le Hung, and Samir Siksek released a paper proving that elliptic curves over real quadratic fields are modular. This result generalizes the celebrated theorem of Wiles, et. al., proving that elliptic curves over Q are modular. I will recall the statement of these theorems and explain how we expect them to generalize to abelian surfaces in the Paramodular Conjecture of Brumer and Kramer. The Paramodular Conjecture is known for surfaces that arise as Weil restrictions of elliptic curves over real quadratic fields by a result of Brooks Roberts and myself.