Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transcendental splitting fields of division algebras   We examine when division algebras can share common splitting fields of
bounded transcendence degree. In particular, we show that one can find fields
for which one has infinitely many Brauer classes of the same index and period
at least $3$, all nonisomorphic and having the same set of splitting fields of
transcendence degree at most $1$. On the other hand, we show that one fixes any
division algebra over a field, then any division algebras sharing the same
splitting fields of transcendence degree at most $3$ must generate the same
cyclic subgroup of the Brauer group. In particular, there are only a finite
number of such division algebras. We also show that a similar finiteness
statement holds for splitting fields of transcendence degree at most $2$.

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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int