The Arakelov Class Group

Speaker: 
Ha Tran
Date: 
Thu, Sep 22, 2016
Location: 
PIMS, University of Calgary
Conference: 
PIMS CRG in Explicit Methods for Abelian Varieties
Abstract: 
Let F be a number field. The Arakelov class group Pic_0 F of F is an analog to the Picard group of a curve. This group provides us the information of F such as the class number h_F, the class group Cl(F) and the regulator R_F. In this talk, we will first introduce Pic_0 F then show that how this group gives us the information of F. Next, we will discuss a tool to compute this group-reduced Arakelov divisors- and their properties. Finally, some open problems relating to this topic will be presented. See the event webpage for more information.