Hensel's lemma for the norm principle for groups of type D_n

Given a finite separable field extension and a linear algebraic group defined over the base field, we can study the "Norm Principle", which examines how the base change of the group behaves with respect to the norm map of the field extension. It remains an open question whether the norm principle holds for all linear algebraic groups. In this talk, we will recall a Galois cohomology approach to this problem, and discuss the norm principle for groups of type D_n, in particular over complete discretely valued fields.