|Date: Friday, April 06, 2018
Location: 3096 East Hall (3:10 PM to 4:00 PM)
Title: The Tate module of an elliptic curve
Abstract: We begin the talk with the classification of the possible endomorphism rings for complex elliptic curves, using their first integral singular homology groups. Then, we move on to positive characteristic. First, we discuss an observation due to Serre that in this setting, we cannot have a reasonable homology theory with integral coefficients. As a remedy, we introduce the Tate module of an elliptic curve. With this new tool at our disposal, we classify the possible endomorphism rings for elliptic curves in arbitrary characteristic. This talk will be accessible to anyone who is in or has taken 632.
Speaker: Emanuel Reinecke