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Grothendieck Rings of ℤ-Valued Fields

Published online by Cambridge University Press:  15 January 2014

Raf Cluckers  and
Deirdre Haskell
Raf Cluckers
Affiliation:
Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Heverlee, BelgiumE-mail:[email protected]
Deirdre Haskell
Affiliation:
Department of Mathematics and Statistics, Mcmaster University, 1280 Main St. West, Hamilton, Ontario, CanadaL8S 4K1, E-mail:[email protected]
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Abstract

We prove the triviality of the Grothendieck ring of a ℤ-valued field K under slight conditions on the logical language and on K. We construct a definable bijection from the plane K2 to itself minus a point. When we specialize to local fields with finite residue field, we construct a definable bijection from the valuation ring to itself minus a point.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 7 , Issue 2 , June 2001 , pp. 262 - 269
Copyright
Copyright © Association for Symbolic Logic 2001

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References

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