arXiv subjects

Yachen Liu

Publications and source records attributed to Yachen Liu.

2 recordsLinked to original sources

arXiv2025

The cohomology of certain intermediate strata of Kottwitz varieties

We derive explicit formulas for the Frobenius-Hecke traces of the etale cohomology of certain strata of Kottwitz varieties (which are certain compact unitary type Shimura varieties considered by Kottwitz), in terms of automorphic representations and certain explicit polynomials. We obtain our results using the trace formula, representations of general linear groups over p-adic fields, and a truncation of the formula of Kottwitz for the number of points on Shimura varieties over finite fields.

math.NT↗

arXiv2024

An automorphic description of the zeta function of the basic stratum of certain Kottwitz varieties

We derive formulas for the number of points on the basic stratum of certain Kottwitz varieties in terms of automorphic representations and certain explicit polynomials, for which we present efficient algorithms for computation. We obtain our results using the trace formula, base change, representations of general linear groups over p-adic fields, and a truncation of the formula of Kottwitz for the number of points on Shimura varieties over finite fields.

math.NT↗