Title
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Nonsplit conics in the reduction of an arithmetic curve
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Author
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Abstract
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For a function field in one variable F/ K and a discrete valuation v of K with perfect residue field k, we bound the number of discrete valuations on F extending v whose residue fields are non-ruled function fields in one variable over k. Assuming that K is relatively algebraically closed in F, we find that the number of non-ruled residually transcendental extensions of v to F is bounded by g + 1 where g is the genus of F/ K. An application to sums of squares in function fields of curves over R((t)) is outlined. |
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Language
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English
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Source (journal)
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Mathematische Zeitschrift. - Berlin, 1918, currens
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Publication
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Berlin
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2024
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ISSN
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0025-5874
[print]
1432-1823
[online]
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DOI
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10.1007/S00209-023-03395-3
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Volume/pages
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306
:1
(2024)
, p. 1-16
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Article Reference
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12
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ISI
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001114308100001
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Full text (Publisher's DOI)
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Full text (open access)
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Full text (publisher's version - intranet only)
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