Grothendieck Rings of ℤ-Valued Fields Academic Article uri icon

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abstract

  • AbstractWe 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.

publication date

  • June 2001