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Grothendieck rings of \mathbb{Z}-valued fields

Raf Cluckers·Deirdre Haskell
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Abstract

We prove the triviality of the Grothendieck ring of a integer-valued field K under slight conditions on the logical language and on K. We construct a definable bijection from the plane K^2 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.

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Raf Cluckers, Deirdre Haskell. 2003-11-25. Grothendieck rings of \mathbb{Z}-valued fields. https://arxiv.org/abs/math/0311435

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