Geometry Seminar

 

University of Tor Vergata, Department of Mathematics

16^th  of January 2024, 14:30-16:00, room “Dal Passo”

 

 

 

 

 

 

 

 

On towers of isogeny graphs with full level structure

 

Katharina Müller
Universität der Bundeswehr München

 

 

 

 

 Let k be a finite field of chracteristic q. Let p,l be primes corpime to q and let N be a positive integer coprime to pql.

In this talk we will define graphs X_l^q(Np^n) whose vertices are tuples (E,P,Q), where E/k is an elliptic curves and P,Q is a basis for E[Np^n]. The edges are given by degree l isogenies. 

We will discuss when X_l^q(Np^n)/X_l^q(Np^{n-1}) is Galois and will describe the structure of these graphs as volcanos.
This is joint work with Antonio Lei.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This talk is part of the activity of the MIUR Excellence Department Projects MathMod@TOV, and the PRIN 2022 Moduli Spaces and Birational Geometry