The interplay between valuations and certain geometrically rational varieties, in particular quadrics, has turned out to be very fruitful for proving that certain subsets of fields are existentially definable or diophantine. In particular, this has been used by J. Koenigsmann to prove that Q\Z is diophantine in Q. His proof combines several ingredients from classical number theory, involving...
In this talk $F$ denotes a field of characteristic $2$, $W_{q}(F)$ the Witt of nonsingular quadratic forms over $F$, $W(F)$ the Witt ring of regular symmetric bilinear forms over $F$. For any integer $m\geq0$, we denote by $I_{q}^{m+1}(F)$ the group $I^{m}F\otimes W_{q}(F)$, where $I^{m}F$ \ is the $m$-th power of the fundamental ideal $IF$ of $W(F)$, and $\otimes$ is the module action of...
