Seminário de Álgebra  RSS

17/07/2012, 15:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
Marco Robalo, Université Montpellier 2

Noncommutative Motives: A universal characterization of the motivic stable homotopy theory of schemes.

In this talk I will explain a new approach to the theory of noncommutative motives based in the construction of a motivic stable homotopy theory for the noncommutative schemes of Kontsevich.

In the first part of the talk, we review the original motivic homotopy theory of schemes as constructed by Voevodsky-Morel-Jardine and explain its recent universal characterization. The fundamental step in this characterization is to understand the nature of the construction of symmetric spectrum objects in a model category M. I will try to sketch the idea in detail.

In the second part we explain the construction of a new motivic theory for the noncommutative schemes which mimics the classical one for schemes. Every scheme gives rise to a noncommutative one and because of the universal property described in the first part, this assignment gives birth to a canonical monoidal comparison map between the commutative and the new noncommutative motivic theories. This work is ongoing and it is part of my PhD thesis under the direction of B. Toën in the Université de Montpellier.

The talk will require (at all times) the language of -categories, for which I will provide a small introduction in the beginning.

References


Organizador actual: Gustavo Granja

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