• M S Raghunathan

Articles written in Proceedings – Mathematical Sciences

• Geometric construction of cohomology for arithmetic groups I

• Principal bundles on the affine line

We prove that any principal bundle on the affine line over a perfect field with a reductive group as structure group comes from the base field by base change.

• Discrete subgroups of algebraic groups over local fields of positive characteristics

It is shown in this paper that ifG is the group ofk-points of a semisimple algebraic groupG over a local fieldk of positive characteristic such that all itsk-simple factors are ofk-rank 1 and Γ ⊂G is a non-cocompact irreducible lattice then Γ admits a fundamental domain which is a union of translates of Siegel domains. As a consequence we deduce that ifG has more than one simple factor, then Γ is finitely generated and by a theorem due to Venkataramana, it is arithmetic.

• 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.

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019