The connectedness of degeneracy loci in positive characteristic - Lodh, Rémi (Comptes Rendus. Mathématique)
A well-known result of Fulton–Lazarsfeld ensures the connectedness of degeneracy loci under an ampleness condition. We extend it to positive characteristic, along with the variants for degeneracy loci of symmetric and alternating maps of even rank, due to Tu in characteristic zero. The proof uses the explicit determination of the top étale cohomology group of an algebraic variety, a result communicated by Esnault.