Abstract:

The aim of this work (joint with M. Papikian) is to investigate the analogue of Mazur's theorem in the context of higher rank Drinfeld modular varieties. In this talk, we shall discuss the cuspidal divisor subgroup of the Picard scheme of the Drinfeld modular varieties of higher rank, and determine the explicit structure for the prime level case. This is an analogue of a result of Ogg for classical modular curves of prime level. Moreover, we further define an Eisenstein ideal in the Hecke algebra acting on the Drinfeld modular Picard scheme, and show that the Eisenstein ideal has finite index in the Hecke algebra.