Department of Mathematics


  •  Oscar Rivero, University of Warwick
  •  Motivic congruences and Sharifi's conjecture
  •  03/31/2021
  •  4:00 PM - 5:00 PM
  •  Online (virtual meeting) (Virtual Meeting Link)
  •  Preston Wake (

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 striking relationship with the first derivative L'(f,0) at the near central point s=0 of the L-series of f. In this talk, 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 motivic part of L'(f,0) modulo p and L''(f,0) modulo p with circular units. The proofs make use of delicate 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.



Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science