|GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR|
|Topic:||A Semistable Model for the Tower of Modular Cures|
|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) .