Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cohomological obstruction theory for Brauer classes and the period-index
  problem   Let U be a connected scheme of finite cohomological dimension in which every
finite set of points is contained in an affine open subscheme. Suppose that
alpha is a class in H^2(U_et,Gm)_{tors}. For each positive integer m, the
K-theory of alpha-twisted sheaves is used to identify obstructions to alpha
being representable by an Azumaya algebra of rank m^2. The etale index of
alpha, denoted eti(alpha), is the least positive integer such that all the
obstructions vanish. Let per(alpha) be the order of alpha in
H^2(U_{et},Gm)_{tors}. Methods from stable homotopy theory give an upper bound
on the etale index that depends on the period of alpha and the etale
cohomological dimension of U; this bound is expressed in terms of the exponents
of the stable homotopy groups of spheres and the exponents of the stable
homotopy groups of B(Z/per(alpha)). As a corollary, if U is the spectrum of a
field of finite cohomological dimension d, then eti(alpha) divides
per(alpha)^[d/2], where [d/2] is the integer part of d/2, whenever per(alpha)
is divided neither by the characteristic of k nor by any primes that are small
relative to d.

18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn