Perverse Leray Filtration

The perverse Leray filtration of an algebraic map is the filtration on cohomology obtained from perverse truncations of its derived direct image. In an unshifted convention it is the image of in . Here is truncation for the middle perverse structure. Shifting the complex changes the index convention, so the normalization must be specified when comparing it to another filtration.

For the smooth coprime fixed-determinant Hitchin fibration with base dimension and total-space dimension , the convention for the P=W conjecture uses and on the base. The P=W conjecture compares the resulting perverse indices with twice those indices in the mixed-Hodge weight filtration.