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arXiv · 1709.00876

On the length of perverse sheaves and D-modules

Nero Budur·Pietro Gatti·Yongqiang Liu·Botong Wang
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Abstract

We prove that the length function for perverse sheaves and algebraic regular holonomic D-modules on a smooth complex algebraic variety Y is an absolute Q-constructible function. One consequence is: for "any" fixed natural (derived) functor F between constructible complexes or perverse sheaves on two smooth varieties X and Y, the loci of rank one local systems L on X whose image F(L) has prescribed length are Zariski constructible subsets defined over Q, obtained from finitely many torsion-translated complex affine algebraic subtori of the moduli of rank one local systems via a finite sequence of taking union, intersection, and complement.

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Nero Budur, Pietro Gatti, Yongqiang Liu, Botong Wang. 2019-03-13. On the length of perverse sheaves and D-modules. https://arxiv.org/abs/1709.00876

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