20 mar 2018 -- 15:00
Aula Magna, DM, Pisa
Seminari di Geometria del Dipartimento di Matematica dell'Università di Pisa
Abstract.
A classical result of Ken Ribet states that an abelian variety defined over the maximal cyclotomic extension of a number field has only finitely many torsion points. In joint work with Damian Rössler we have proven a finiteness theorem for the cohomology of algebraic varieties defined over fields of the above type which is a broad generalization of Ribet's theorem. We have also made some conjectures concerning possible generalizations involving algebraic cycles, and investigated analogues in positive characteristic. I'll give an introduction to this fascinating subject, emphasizing ideas rather than technicalities.