From Rational points to étale homotopy fixed points

https://hu-berlin.zoom.us/j/61339297016

To decide whether integral or rational solutions to polynomial equations exist is a classical problem in mathematics. Such solutions correspond to what we now call rational points on algebraic varieties. To detect such points is still a notoriously difficult task. In this talk we will build a bridge from rational points to homotopy theory and discuss how étale homotopy fixed points under the Galois action can be used to define obstructions for the existence of rational points. Along the way we will review ideas from étale homotopy theory and review the difference between fixed and homotopy fixed points under group actions.