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- W1979767874 abstract "Suppose that K is a function field of a conic over a subfield K 0 . Let v 0 be a valuation of K 0 with residue field k 0 of characteristic ≠2. Let v be an extension of v 0 to K having residue field k . It has been proved that either k is an algebraic extension of k 0 or k is a regular function field of a conic over a finite extension of k 0 . This result can also be deduced from the genus inequality of Matignon (cf. [On valued function fields I, Manuscripta Math. 65 (1989), 357–376]) which has been proved using results about vector space defect and methods of rigid analytic geometry. The proof given here is more or less self-contained requiring only elementary valuation theory." @default.
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- W1979767874 date "1993-10-01" @default.
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- W1979767874 title "Residue fields of valued function fields of conics" @default.
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- W1979767874 doi "https://doi.org/10.1017/s0013091500018551" @default.
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