Andrei Druzhinin (Chebyshev Laboratory, St. Petersburg State University): Vanishing results for negative motivic homotopy groups

We discuss the vanishing of the negative S¹-stable and P¹-stable motivic homotopy groups over a base scheme S, and the Morel’s connectivity theorem. We discuss the ordinal Morel’s proof and the generations. We compare the formulas for motivically fibrant replacements in S¹-stable and P¹-stable cases that implies the vanishing, and touch the techniques of unramified sheaves and of transfers used in many significant researches to control the interaction of the Nisnevich and A¹-localisations.