Gluing of perverse sheaves on the basic affine space

Details Gluing of perverse sheaves on the basic affine space Gluing of perverse sheaves on the basic affine space

1998-11-25

arxiv.org/abs/math/9811155v2

Mathematics

Algebraic Geometry

48 pages, AMSLatex, appendix (coauthored with Roman Bezrukavnikov) and reference added, minor revision of the main text

Scientific paper

This paper is devoted to the study of the gluing construction for perverse sheaves on $G/U$ introduced by Kazhdan and Laumon ($G$ is a semisimple gourp, $U$ is the unipotent radical of a Borel subgroup in $G$). Kazhdan and Laumon conjectured that all Ext-groups in the glued category are finite-dimensional and that global cohomological dimension is finite. We prove the first part of this conjecture. In the appendix we show that the simple object in the glued category corresponding to the constant sheaf has infinite cohomological dimension, thus disproving the second part of the above conjecture.

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