Title: On the length of perverse sheaves and D-modules,
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.