Abstract for the talk on 01.03.2018 (10:00 h)Seminar on Nonlinear Algebra
Avinash Kulkarni (Simon Fraser University, Burnaby)
The arithmetic of uniquely trigonal genus 4 curves
Number ﬁelds, which are ﬁnite ﬁeld extensions of the ﬁeld of rational numbers, are fundamental objects of study in number theory. One of the most important invariants of a number ﬁeld is the class group, which measures how close the ring of integers of that number ﬁeld is to being a unique factorization domain. Despite their importance, class groups remain mysterious objects in number theory. This talk will demonstrate how the titular family of curves can be used to construct cubic number ﬁelds with interesting class groups.
Background: The talk is designed for a general level mathematics colloquium. Some algebraic number theory or algebraic geometry is useful, but not necessary.