Algebra Seminar

Speaker: Senate Meeting - No Seminar (Western)

"no seminar"

Time: 14:30

Room: MC 108

Algebra Seminar

Speaker: Elyes Boughattas (Université Sorbonne Paris Nord - Paris XIII)

"Purity of strong approximation over C(t)"

Time: 14:30

Room: ZOOM

Strong approximation theorems are ubiquitous in arithmetic geometry and have been broadly studied over global fields. But what happens if the base field is replaced by the function field of a complex algebraic curve? This question has been tackled since the last decade, using the deformation theory of algebraic curves. In this presentation, we shall give some generalities on strong approximation for varieties over $\mathbf{C}(t)$ and discuss the remanence of this property on the complementary of any closed subset of codimension 2.

Algebra Seminar

Speaker: Haowen Zhang (Jussieu University)

"Weak approximation for homogeneous spaces over C((X,Y)) or C((X))(Y)"

Time: 14:30

Room: ZOOM

We study obstructions to weak approximation for connected linear groups and homogeneous spaces with connected or abelian stabilizers over finite extensions of C((X,Y)) or functions fields of curves over C((X)). We show that for connected linear groups, the usual Brauer-Manin obstruction works as in the case of tori, using some dévissage argument. However, this Brauer-Manin obstruction is not enough for homogeneous spaces, and we should somehow combine the Brauer-Manin obstruction with the descent obstruction using torsors under quasi-trivial tori, another natural tool used in the study of such questions, as done by Izquierdo and Lucchini Arteche for the study of obstruction to rational points.