The rigidity property for the chain complex of a torus in A1-homotopy theory, and the Friedlander-Milnor conjecture

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• Fabien Morel (Munich)
• Wednesday 01 December 2010, 14:15-15:15
• MR13, CMS.

If you have a question about this talk, please contact Burt Totaro.

In this talk we prove that the chain complex of a product of G_m’s in A1-homotopy theory satisfies the rigidity property at any prime l different from the characteristic of the base field, by first explaining how the homology sheaves of this complex have a structure of “A1-sheaves with generalized transfers”, more general than the notion of A1-invariant sheaves with transfers due to V. Voevodsky. We prove that such sheaves also have the rigidity property mod l by reducing in a non-trivial way to the classical rigidity theorem. This step is one of the main technical parts of our proof of the Friedlander-Milnor conjecture for groups of small rank like SL_2 and SL_3.

This talk is part of the Algebraic Geometry Seminar series.

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