Modular intersection cohomology of Drinfeld's compactifications

TL;DR

This paper calculates the dimensions of intersection cohomology stalks on Zastava schemes and Drinfeld compactifications for reductive groups, showing these dimensions are independent of the coefficient field in good characteristic.

Contribution

It provides explicit dimension formulas for intersection cohomology stalks on these moduli spaces, revealing their independence from the coefficient field in good characteristic.

Findings

Dimensions are explicitly computed for stalks of intersection cohomology complexes.

Dimensions do not depend on the choice of coefficient field in good characteristic.

Results apply to Zastava schemes and Drinfeld compactifications associated with reductive groups.

Abstract

We compute the dimension of the cohomology of stalks of intersection cohomology complexes on Zastava schemes and Drinfeld compactifications associated with a connected reductive algebraic group $G$, in case the characteristic of the coefficients field $\Bbbk$ is good for $G$. In particular, we show that these dimensions do not depend on the choice of $\Bbbk$.