2005
DOI: 10.1016/j.top.2005.02.005
|View full text |Cite
|
Sign up to set email alerts
|

Topological methods for complex-analytic Brauer groups

Abstract: 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. 1991 Mathematics Subject Classification. 14F22, 20J06, 32J15.Theorem. Let X be a complex Lie group or … Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

0
37
0

Year Published

2014
2014
2024
2024

Publication Types

Select...
7
1
1

Relationship

1
8

Authors

Journals

citations
Cited by 28 publications
(37 citation statements)
references
References 51 publications
0
37
0
Order By: Relevance
“…The Brauer groups exist in complex analytic topological spaces and the equality between Brauer groups in view of geometry is evaluated in [5]. If the complex analytic topological space X = Y an is compact, then the canonical map between Brauer groups f : Br(Y) → Br(X) is invertible.…”
Section: Topology Of Complex Analytic Spacesmentioning
confidence: 99%
“…The Brauer groups exist in complex analytic topological spaces and the equality between Brauer groups in view of geometry is evaluated in [5]. If the complex analytic topological space X = Y an is compact, then the canonical map between Brauer groups f : Br(Y) → Br(X) is invertible.…”
Section: Topology Of Complex Analytic Spacesmentioning
confidence: 99%
“…It follows from [28,Proposition 1.3] that Br ′ (X) is isomorphic to the analytic cohomological Brauer group Br ′ (X an ), the torsion part of H 2 (X an , O × Xan ). The exponential sequence 0 → Z → O Xan → O × Xan → 1 induces the following exact sequence:…”
Section: A Characterization In Terms Of Divisor Class Groups and Braumentioning
confidence: 99%
“…• The best result for complex spaces is the result of Schröer [47] which gives a purely topological condition that ensures Br(X an ) = Br ′ (X an ). This condition applies to complex Lie groups, Hopf manifolds, and all compact complex surfaces except for a class which conjecturally does not exist, namely the class VII surfaces that are not Hopf surfaces, Inoue surfaces, or surfaces containing a global spherical shell.…”
Section: A Problem Of Grothendieckmentioning
confidence: 99%