Seminar

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In his study of quadratic forms, Milnor conjectured that certain motivic cohomology groups appear as the graded pieces of the filtration by powers of the fundamental ideal on the Witt ring of symmetric bilinear forms. This conjecture was proved by Kato for fields of characteristic 2 and by Orlov–Vishik–Voevodsky and Morel for fields of other characteristics. In this talk, I will present an analogue of this conjecture for local rings that are not necessarily fields, with particular emphasis on mixed characteristic 2. As an application, over any unramified regular local ring, this produces syntomic cohomological invariants of symmetric bilinear forms.