Additive combinatorics using equivariant cohomology

We introduce a geometric method to study additive combinatorial problems. Using equivariant cohomology we reprove the Dias da Silva–Hamidoune theorem. We improve a result of Sun on the linear extension of the Erdős–Heilbronn conjecture. We generalize a theorem of G. Kós (the Grashopper problem) which in some sense is a simultaneous generalization of the Erdős–Heilbronn conjecture. We also prove a signed version of the Erdős—Heilbronn conjecture and the Grashopper problem. Most identities used are based on calculating the projective degree of an algebraic variety in two different ways.