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Columbia University
Algebraic Geometry Seminar
Johan deJong
MIT
The period-index problem for surfaces
Let k be an algebraically closed field. Tsen’s theorem says that any BrauerSeveri variety over a curve over k has a section. We’ll discuss an analog
for surfaces over k. Namely, given an element x of order n in the Brauer
group of a smooth surface S, there should be a Brauer-Severi variety of
relative dimension n − 1 over S representing x. This is called the periodindex problem (for the surface S and the class x). The period index problem
has a negative solution when the base has dimension 3 or more.
Friday, February 8, 2002
2:30pm
Mathematics 417
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