Combinatorics

Pure mathematics

Mathematics

Algebra over a field

Abelian group

Rank (graph theory)

Rank of an abelian group

Elementary abelian group

Annales Scientifiques de l École Normale Supérieure

Generalizing the continuous rank function of Barja-Pardini-Stoppino, in this paper we consider cohomological rank functions of Q-twisted (complexes of) coherent sheaves on abelian varieties.They satisfy a natural transformation formula with respect to the Fourier-Mukai-Poincaré transform, which has several consequences.In many concrete geometric contexts these functions provide useful invariants.We illustrate this with two different applications, the first one to GVsubschemes and the second one to multiplication maps of global sections of ample line bundles on abelian varieties.

Cohomological rank functions on abelian varieties