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Modular intersection cohomology of Drinfeld's compactifications

Pramod N. Achar, Gurbir Dhillon, Simon Riche

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 $\Bbbk$.

Modular intersection cohomology of Drinfeld's compactifications

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 , in case the characteristic of the coefficients field is good for . In particular, we show that these dimensions do not depend on the choice of .

Paper Structure

This paper contains 45 sections, 29 theorems, 277 equations.

Table of Contents

  1. Introduction
  2. Drinfeld's compactifications
  3. Relation with semiinfinite sheaves
  4. Drinfeld's compactifications and the semiinfinite flag variety
  5. Contents
  6. Acknowledgements
  7. Preliminaries
  8. Group-theoretic data
  9. Symmetric powers of curves
  10. Étale maps of curves
  11. Ysucceq0-graded symmetric powers of curves
  12. Torsors
  13. Stacks of torsors
  14. Affine Grassmannian and semiinfinite orbits
  15. Drinfeld's compactification
  16. ...and 30 more sections

Key Result

Lemma 2.1

Let $\mathbf{a}$ be a partition of $n$, and write it as with $a_1, \ldots, a_k$ all distinct. Then there is an isomorphism of schemes

Theorems & Definitions (67)

  • Remark 1.1
  • Remark 1.2
  • Lemma 2.1
  • Lemma 2.2
  • proof
  • Lemma 2.3
  • Lemma 2.4
  • Lemma 2.5
  • Lemma 2.6
  • Remark 2.7
  • ...and 57 more