The canonical subgroup: a "subgroup-free" approach

Beyond the crucial role they play in the foundations of the theory of overconvergent modular forms, canonical subgroups have found new applications to analytic continuation of overconvergent modular forms. For such applications, it is essential to understand various ``numerical'' aspects of the canonical subgroup, and in particular, the precise extent of its overconvergence. We develop a theory of canonical subgroups for a general class of curves (including the unitary and quaternionic Shimura curves), using formal and rigid geometry. In our approach, we use the common geometric features of these curves rather than their (possible) specific moduli-theoretic description.Comment: 16 pages, 1 figur

The congruence subgroup problem

This is a short survey of the progress on the congruence subgroup problem since the sixties when the first major results on the integral unimodular groups appeared. It is aimed at the non-specialists and avoids technical details.Comment: 10 page

The Schur-Clifford subgroup of the Brauer-Clifford group

We define a Schur-Clifford subgroup of Turull's Brauer-Clifford group, similar to the Schur subgroup of the Brauer group. The Schur-Clifford subgroup contains exactly the equivalence classes coming from the intended application to Clifford theory of finite groups. We show that the Schur-Clifford subgroup is indeed a subgroup of the Brauer-Clifford group, as are certain naturally defined subsets. We also show that this Schur-Clifford subgroup behaves well with respect to restriction and corestriction maps between Brauer-Clifford groups.Comment: Corrected a few typos. Final versio

Township Residents!

A pamphlet explaining why the End Conscription Campaign is fasting and praying for South African Township residents as the South African Defence Force maintains a presence in the townships.https://digitalcommons.colum.edu/ecc/1011/thumbnail.jp