On a query of Adrian Wadsworth

Khanduja, Sudesh K. ; Garg, Usha (1999) On a query of Adrian Wadsworth Indian Journal of Pure and Applied Mathematics, 30 (9). pp. 945-949. ISSN 0019-5588

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Abstract

Lei v0 be a valuation of a field K0 with residue field k0 of characteristic #2. Suppose that K is a function field of a conic over K0 and v is a prolongation of v0 to K. whose residue field k is not algebraic over k0. It is well known (cf [Residue fields of valued function fields of conies, Proc. Edinb. math. Sac 36 (1993), 469-78]) that either k is a simple transcendental extension of a finite extension of k0,or k is a regular function field of a conic over k0. The paper contains the answer to a natural question posed by Wadsworth which states that if v1, v1 are any two prolongations of v0 to K with residue fields k1 k2 non-algebraic over k0 such that neither k1, or k2 is a simple transcendental extension of a finite extension of k0, is it true that k1, is t0-isomorphic to kT.

Item Type:Article
Source:Copyright of this article belongs to Indian National Science Academy.
Keywords:Valued Fields; Valuations and their Generalization
ID Code:83983
Deposited On:23 Jun 2012 15:03
Last Modified:19 May 2016 00:37

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