This Thursday at U. Haifa Topology & Geometry seminar on February 28, 2019 at 12:10
Geometry & Topology Seminar
Speaker: Shachar Carmeli (The Weizmann Institute of Science)
Topic: Etale Obstructions to Rational Points on Arithmetic Spheres
Place: room 614 in the Science & Education Building
Time 12:10
Date: Thursday, February 28, 2019
Abstract:
Etale homotopy theory attaches to every algebraic variety X over a field F a homotopy type E’t(X) called the etale homotopy type.
This construction was generalized by Schlank and Barnea to the relative case, and attached with every algebraic variety over X a sequence of obstructions to rational points leaving in certain Galois cohomology groups.
I will introduce relative etale homotopy theory from an infinity-categorical perspective, and the relevant obstruction theory. Then I will present our computation of the (mod 2) lowest obstruction to solutions of quadratic equations in many variables over F. This is a joint work with Edo Arad and Tomer Schlank.
