Grothendieck Rings of $\mathbb{Z}$-Valued Fields

Cluckers, Raf; Haskell, Deirdre

Bull. Symbolic Logic, Tome 7 (2001) no. 1, p. 262-269 / Harvested from Project Euclid

Résumé

We prove the triviality of the Grothendieck ring of a $\mathbb{Z}$-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 specialized to local fields with finite residue field, we construct a definable bijection from the valuation ring to itself minus a point.

Publié le : 2001-06-14
Classification:

@article{1182353778,
     author = {Cluckers, Raf and Haskell, Deirdre},
     title = {Grothendieck Rings of $\mathbb{Z}$-Valued Fields},
     journal = {Bull. Symbolic Logic},
     volume = {7},
     number = {1},
     year = {2001},
     pages = { 262-269},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1182353778}
}

Cluckers, Raf; Haskell, Deirdre. Grothendieck Rings of $\mathbb{Z}$-Valued Fields. Bull. Symbolic Logic, Tome 7 (2001) no. 1, pp.  262-269. http://gdmltest.u-ga.fr/item/1182353778/