Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Azumaya algebras with involution and classical semisimple group schemes   Let $S$ be a non-empty scheme with 2 invertible. In this paper we present a
functor $F: AZ_*^{n'} \rightarrow GS_*^n$ where $AZ_*^{n'}$ and $GS_*^n$ are
fibered categories over $Sch_S$ given respectively by degree $n'$ Azumaya
algebras with an involution of type $*$ and rank $n$ adjoint group schemes of
classical type $*$ with absolutely simple fibers. Here $n'$ is a function of
$n$. We show that this functor is an equivalence of fibered categories using
\etale descent, thus giving a classification of adjoint (as well as simply
connected) groups schemes over $S$, generalizing the well known case when the
base scheme is the spectrum of a field. In particular, this implies that every
adjoint group scheme of classical type with absolutely simple fibers is
isomorphic to the neutral component of automorphism group scheme of a unique
(up to isomorphism) Azumaya algebra with involution. We also show interesting
applications of this classification such as specialization theorem for
isomorphism classes of Azumaya algebra with involution over Henselian local
rings, uniqueness of integral model for groups with good reduction over
discrete valued fields and discuss its implications on the Grothendieck-Serre
conjecture over certain domains.

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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex