A Semistable Model for the Tower of Modular Cures

GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR
Topic:A Semistable Model for the Tower of Modular Cures
Speaker:Jared Weinstein
Affiliation:Member, School of Mathematics
Date:Wednesday, October 27
Time/Room:2:15pm - 3:15pm/S-101

The usual Katz-Mazur model for the modular curve X(p^n) has horribly singular reduction. For large n there isn't any model of X(p^n) which has good reduction, but after extending the base one can at least find a semistable model, which means that the special fiber only has normal crossings as singularities. We will reveal a new picture of the special fiber of a semistable model of the entire tower of modular curves. We will also indicate why this problem is important from the point of view of the local Langlands correspondence for GL(2) .