BIMSA > BIMSA-YMSC Tsinghua Number Theory Seminar Eisenstein congruences and Euler systems
Eisenstein congruences and Euler systems
Organizers
Yueke Hu , Emmanuel Lecouturier , Cezar Lupu
Speaker
Oscar Rivero Salgado
Time
Friday, October 22, 2021 4:00 PM - 5:00 PM
Venue
1118
Online
Zoom 849 963 1368 (YMSC)
Abstract
Let f be a cuspidal eigenform of weight two, and let p be a prime at which f is congruent to an Eisenstein series. Beilinson constructed a class arising from the cup-product of two Siegel units and proved a relationship with the first derivative of the L-series of f at the near central point s=0. I will motivate the study of congruences between modular forms at the level of cohomology classes, and will report on a joint work with Victor Rotger where we prove two congruence formulas relating the Beilinson class with the arithmetic of circular units. The proofs make use of Galois properties satisfied by various integral lattices and exploits Perrin-Riou's, Coleman's and Kato's work on the Euler systems of circular units and Beilinson-Kato elements and, most crucially, the work of Fukaya-Kato around Sharifi’s conjectures.