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Motivic invariants of birational maps

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KAH2 - K-theory, algebraic cycles and motivic homotopy theory

I explain how exceptional divisors of birational maps can be assembled into invariants taking values in the Grothendieck ring of varieties and in the Kontsevich-Tschinkel ring. Using these invariants we prove new results about the structure of the groups of birational isomorphisms, in particular, we prove that various Cremona groups are not generated by regularizable elements. This is joint work with H.-Y. Lin.

This talk is part of the Isaac Newton Institute Seminar Series series.

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