On the Artin vanishing theorem for Stein spaces

2024/10/05 by Benoist, Olivier
#32C18 #32E10 #32E30 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.04291

Abstract

Artin vanishing theorems for Stein spaces refer to the vanishing of some of their (co)homology groups in degrees higher than the dimension. We obtain new positive and negative results concerning Artin vanishing for the cohomology of a Stein space relative to a Runge open subset. We also prove an Artin vanishing theorem for the Gal(C/R)-equivariant cohomology of a Gal(C/R)-equivariant Stein space relative to the fixed locus.

Related

• Artin vanishing in rigid analytic geometry
• Notions of Stein spaces in non-archimedean geometry
• On the v-Picard group of Stein spaces
• Variation on Artin's vanishing theorem
• Vanishing of temperate cohomology on complex manifolds