The main result is that the Jacobian of the Drinfeld modular curve X_1(n) associated to the prime n\in {F}_q[T] and the congruence subgroup \Gamma_1(n) of GL(2)) has connected reduction modulo the place n. This determines one of the bad Tamagawa factors in the L-function of the Jacobian. The proof rests on constructing a function field analogue of the Igusa curves which describe the bad reduction of elliptic modular curves, as well as on the resolution of cyclic quotient singularities on arithmetic surfaces.
Algebra Seminar
Monday, October 16, 2006 - 4:00pm
Sreekar Shastry
Tata Institute of Fundamental Research