Higher Etale obstructions are cohomological obstructions introduced by Yonatan Harpaz and Tomer Schlank for solutions of algebraic equations over a field. Their definition is based on the theory of relative etale homotopy type. In my talk I will explain the construction of relative etale homotopy type and the resulting obstruction theory.
I will also present the calculation of these obstructions for quadratic equations of the form a_1x_1^2 + ... + a_nx_n^2 = 1. This is a joint work with Edo Arad and Tomer Schlank.