Number Theory Seminar – University of Copenhagen

Number Theory Seminar

Speaker: Marc Hindry (Paris 7 Denis Diderot)

Title: Analogue of the Brauer-Siegel Theorem for abelian varieties: similarities and differences.

Abstract: The classical Brauer-Siegel theorem states that for a sequence of number fields with, say, bounded degree, the product of the class number by the regulator of units behaves asymptotically like the square root of the discriminant. The analogue for abelian varieties of a given dimension defined over a global field (a number field or a function field over a finite field) replaces the three quantities by respectively the cardinality of the Shafarevich-Tate group, the Néron-Tate height regulator and the exponential height. I will describe all the objects involved, discuss the possible analogues and explain why a similar upper bound is "almost certain" and a similar lower bound unlikely.