Santiago Arango-Piñeros : Trace distributions and Galois groups of Frobenius polynomials

Posted by Frederick Saia , part of the Number Theory Seminar.

At

Dec. 6, 2024, 9 a.m.

In

636 SEO

Abstract

I will discuss the multiplicative group generated by the roots of a monic polynomial with integer coefficients. In particular, I will focus on polynomials that arise as the characteristic polynomial of the Frobenius endomorphism of an abelian variety defined over a finite field. I will discuss some recent results and applications obtained in joint work with Bhamidipati and Sankar (https://arxiv.org/abs/2306.02237), and with Frengley and Vemulapalli (https://sarangop1728.github.io/GaloisGroupsFrobPolys_version0.pdf).