## Postnikov towers in motivic homotopy theory

### Mardi 11 octobre 2011 16:00-17:00 - Levine Marc - Universität Duisburg-Essen

Résumé : Voevodsky has defined a version of the classical Postnikov tower in the motivic stable homotopy category, called the slice tower. Up to now, most of the computations have been for familiar theories, such as algebraic K-theory, where the slice tower gives a « coordinate free » construction of the spectral sequence from motivic cohomology to K-theory. We will look at the properties of the slice tower for very different types of objects, namely, the suspension spectra of smooth varieties. We describe our computation of the induced filtration on $pi_0$ of the sphere spectrum and show that the slice tower converges for suspension spectra of smooth varieties, assuming the base field has finite Galois cohomological dimension.

Lieu : bât. 425 - 113-115

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 Département de Mathématiques Bâtiment 307 Faculté des Sciences d'Orsay Université Paris-Saclay F-91405 Orsay Cedex Tél. : +33 (0) 1-69-15-79-56 Département Fermeture du département Laboratoire Formation