Number Theory Days in Lille

Session

Quadratic forms

10 juil. 2019, 09:00

Salle de réunion (Université de Lille)

48. Quadratic forms and diophantine sets

Karim Johannes Becher (Universiteit Antwerpen)

10/07/2019 09:45

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...

41. Quadratic and Differential Forms over fields of characteristic 2

Roberto Aravire (Universidad Arturo Prat)

10/07/2019 11:00

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...