2017/08/24 by David Hansen, David J. Hansen, Hansen, David
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AG #math.NT
paper · pdf · doi:10.48550/arxiv.1708.07276
19 pages; comments welcome
arxiv created 2017/08/24 · arxiv updated 2017/08/25
We prove a rigid analytic analogue of the Artin vanishing theorem. Precisely, we prove (under mild hypotheses) that the geometric etale cohomology of any Zariski-constructible sheaf on any affinoid rigid space X vanishes in all degrees above the dimension of X. Along the way, we show that branched covers of normal rigid spaces can often be extended across closed analytic subsets, in analogy with a classical result for complex analytic spaces. We also prove a general comparison theorem relating the algebraic and analytic etale cohomologies of any affinoid rigid space.