Department of Mathematics

Algebra

  •  Ken Ribet, UC Berkeley
  •  Cyclotomic torsion points on abelian varieties over number fields
  •  10/21/2022
  •  3:00 PM - 4:00 PM
  •  C304 Wells Hall
  •  Preston Wake (wakepres@msu.edu)

Over 40 years ago, I proved the finiteness of the group of cyclotomic torsion points on an abelian variety over a number field. (A torsion point is cyclotomic if its coordinates lie in the field obtained by adjoining all roots of unity to the base field.) If the abelian variety is one that we know well, and if the number field is the field of rational numbers, we can hope to determine explicitly the group of its cyclotomic torsion points. I will illustrate this theme in the situation studied by Barry Mazur in his landmark "Eisenstein ideal" article, i.e., that where the abelian variety is the Jacobian of the modular curve $X_0(p)$.

 

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