University of Georgia

Mathematics Department Colloquium

Gerard van der Geer

University of Amsterdam

October 28, 1999

The Theta Divisor of a Number Field


Abstract: The topic of this talk is the analogy between number fields and function fields. Although this analogy was discovered in the nineteenth century, and was studied by Weil, Tate, Arakelov and many others, it is by no means fully understood. We shall start by explaining this analogy and then turn to the question of what is the analogue of the geometry of the theta divisor, that plays such a prominent role in the study of curves and Riemann surfaces. I will sketch an approach which was developed in joint work with R. Schoof.