MATH Seminar
| Title: Galois theory of iterated endomorphisms |
|---|
| Seminar: Algebra and Number Theory |
| Speaker: Jeremy Rouse of Wake Forest |
| Contact: Ken Ono, ono@mathcs.emory.edu |
| Date: 2010-10-05 at 3:00PM |
| Venue: MSC E408 |
| Download Flyer |
| Abstract: The basic question we study is the following. Given an abelian algebraic group $A$ defined over $\mathbf{Q}$, a point $\alpha$ in $A(\mathbf{Q})$, and a prime $\ell$, what fraction of primes $p$ have the property that the reduced point $\alpha$ in $A(\mathbf{F}_p)$ has order coprime to $\ell$? Associated with the choice $\alpha$ and $\ell$ is an arboreal Galois representation. We give surjectivity criteria for this representation and use these to answer the question above in many examples where $A$ is an algebraic torus or an elliptic curve. |
See All Seminars