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The Nisnevich topology and the Thom isomorphism

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If you have a question about this talk, please contact Andreas Holmstrom.

To begin with, I will aim to give a memorable definition of the Nisnevich topology, illustrate it with some examples and highlight some important properties. In the second half of the talk I will sketch a proof of the Thom isomorphism in A^1-homotopy: given a closed smooth subvariety Z of a smooth variety X, the quotient X/(X-Z) is homotopy equivalent to the Thom space of the normal bundle of Z in X. In topology this is an easy consequence of the existence of tubular neighbourhoods. The algebraic proof uses a “deformation to the normal bundle” construction and relies heavily on the use of the Nisnevich topology.

This talk is part of the Motivic stable homotopy theory study group series.

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