Khanduja, Sudesh K. ; Usha , Garg
(1993)
*Residue fields of valued function fields of conics*
Proceedings of the Edinburgh Mathematical Society, 36
(3).
pp. 469-478.
ISSN 0013-0915

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Official URL: http://journals.cambridge.org/action/displayAbstra...

Related URL: http://dx.doi.org/10.1017/S0013091500018551

## 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.

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ID Code: | 69888 |

Deposited On: | 17 Nov 2011 03:38 |

Last Modified: | 17 Nov 2011 03:38 |

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