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Residue fields of valued function fields of conics

Published online by Cambridge University Press:  20 January 2009

Sudesh K. Khanduja  and
Usha Garg
Sudesh K. Khanduja
Affiliation:
Centre for Advanced Study in Mathematics, Panjab University, Chandigarh—160014, India
Usha Garg
Affiliation:
Centre for Advanced Study in Mathematics, Panjab University, Chandigarh—160014, India
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Abstract

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Suppose that K is a function field of a conic over a subfield K0. Let v0 be a valuation of K0 with residue field k0 of characteristic ≠2. Let v be an extension of v0 to K having residue field k. It has been proved that either k is an algebraic extension of k0 or k is a regular function field of a conic over a finite extension of k0. 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.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 36 , Issue 3 , October 1993 , pp. 469 - 478
Copyright
Copyright © Edinburgh Mathematical Society 1993

References

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