Stable étale realization and étale cobordism

• Autores: Gereon Quick
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 214, Nº 2, 2007, págs. 730-760
• Idioma: inglés
• DOI: 10.1016/j.aim.2007.03.005
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• Resumen

  • We show that there is a stable homotopy theory of profinite spaces and use it for two main applications. On the one hand we construct an étale topological realization of the stable A 1 -homotopy theory of smooth schemes over a base field of arbitrary characteristic in analogy to the complex realization functor for fields of characteristic zero. On the other hand we get a natural setting for étale cohomology theories. In particular, we define and discuss an étale topological cobordism theory for schemes. It is equipped with an Atiyah-Hirzebruch spectral sequence starting from étale cohomology. Finally, we construct maps from algebraic to étale cobordism and discuss algebraic cobordism with finite coefficients over an algebraically closed field after inverting a Bott element.