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A ruled residue theorem for function fields of conics |
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| Authors: | Parul Gupta Karim Johannes Becher |
| Institution: | 1. Universiteit Antwerpen, Departement Wiskunde, Middelheimlaan 1, 2020 Antwerpen, Belgium;2. IISER Pune, Dr. Homi Bhabha Road, Pashan, Pune 411 008, India;1. Department of Mathematics, William & Mary, Williamsburg, VA 23187, USA;2. Department of Mathematics, Computer and Information Science, SUNY College at Old Westbury, Old Westbury, NY 11568, USA;1. University of Virginia, United States of America;2. Bucknell University, United States of America |
| Abstract: | The ruled residue theorem characterises residue field extensions for valuations on a rational function field. Under the assumption that the characteristic of the residue field is different from 2 this theorem is extended here to function fields of conics. The main result is that there is at most one extension of a valuation on the base field to the function field of a conic for which the residue field extension is transcendental but not ruled. Furthermore the situation when this valuation is present is characterised. |
| Keywords: | Valuation Residue field extension Gauss extension Rational function field Algebraic function field Genus zero Quaternion algebra |
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