Algebraic Geometry Seminar

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Local-global principles for gerbes and homogeneous spaces over semi-global fields

Speaker: Bastian Haase, Emory University

Location: Warren Weaver Hall 317

Date: Tuesday, March 6, 2018, 3:30 p.m.

Synopsis:

Let F be a semi-global field, i.e. a function field of an arithmetic curve. In 2007, Harbater and Hartmann introduced a patching setup for semi-global fields. This patching setup also introduced a notion of local-global principle for varieties over F analogous to the one over global fields. Given a homogeneous space X under a linear algebraic group G over the function field of an arithmetic curve (i.e. a semi-global field), we will discuss when they satisfy a local-global principle. We will study this question by studying the associated quotient stack [X/G]. As this stack is in fact a gerbe, we will discuss local-global principles for gerbes and their relation to bitorsors.