Topological methods for complex-analytic Brauer groups

Details Topological methods for complex-analytic Brauer groups Topological methods for complex-analytic Brauer groups

2004-05-12

arxiv.org/abs/math/0405223v3

Topology 44 (2005), no. 5, 875--894

Mathematics

Algebraic Geometry

20 pages, minor corrections, to appear in Topology

Scientific paper

Using methods from algebraic topology and group cohomology, I pursue Grothendieck's question on equality of geometric and cohomological Brauer groups in the context of complex-analytic spaces. The main result is that equality holds under suitable assumptions on the fundamental group and the Pontrjagin dual of the second homotopy group. I apply this to Lie groups, Hopf manifolds, and complex-analytic surfaces.

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