On Kim's Assumption A over function fields

TL;DR

This paper proves Kim's Assumption A for split classical groups over function fields in positive characteristic, extending to more general classical groups under certain local-global conditions.

Contribution

It establishes Kim's Assumption A for classical groups in positive characteristic, including quasi-split and generalized spinor groups, under local Ramanujan bounds.

Findings

Kim's Assumption A is proven for split classical groups in positive characteristic.

Results hold for groups of classical kind under local-global restrictions.

The work extends the validity of Kim's Assumption A to broader classical groups.

Abstract

We prove Kim's Assumtion A for the split classical groups in positive characteristic. Actually, we work in the slightly more general setting of groups of classical kind, which includes quasi-split classical groups and generalized spinor groups. We establish our results whenever a local Ramanujan bound holds; a bound that is known for the split classical groups in characteristic $p$, and we prove it for groups of classical kind under a local-global restriction.