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Variétés rationnelles

Horaires : Le vendredi 22 janvier 2010, 16h-17h

Lieu : Institut Henri Poincaré, salle 314

Rational points, 0-cycles and S1 spectra

Marc LEVINE (Essen)

Our motivating question is: how can one construct invariants that distinguish between the existence of a rational point and the existence of a 0-cycle of degree 1 on some variety X. We look at this question through the lens of motivic homotopy theory. Here one can use an analog of the classical Postnikov tower to study properties of the 'S1-stable homotopy type' of a variety X. For some special X, this breaks up the homotopy type of X into pieces which can be understood as motives, and thus gives invariants which can be used for a study of the motivating question.

 

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