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University of Cambridge > Talks.cam > Algebraic Geometry Seminar > The rigidity property for the chain complex of a torus in A1-homotopy theory, and the Friedlander-Milnor conjecture

## The rigidity property for the chain complex of a torus in A1-homotopy theory, and the Friedlander-Milnor conjectureAdd to your list(s) Download to your calendar using vCal - 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. ## This talk is included in these lists:- Algebraic Geometry Seminar
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