Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Picard-Vessiot Extensions of Real Differential Fields   For a linear differential equation defined over a formally real differential
field K with real closed field of constants k, Crespo, Hajto and van der Put
proved that there exists a unique formally real Picard- Vessiot extension up to
K-differential automorphism. However such an equation may have Picard-Vessiot
extensions which are not formally real fields. The differential Galois group of
a Picard-Vessiot extension for this equation has the structure of a linear
algebraic group defined over k and is a k-form of the differential Galois group
H of the equation over the differential field K(i), where i denotes a square
root of -1 in the algebraic closure of k. These facts lead us to consider two
issues: determining the number of K-differential isomorphism classes of
Picard-Vessiot extensions and describing the variation of the differential
Galois group in the set of k-forms of H. We address these two issues in the
cases when H is a special linear, a special orthogonal, or a symplectic linear
algebraic group and conclude that there is no general behaviour.

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The categories of this paper are: alg-geom
3
The categories of this paper are: physics
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The categories of this paper are: econ
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph