Stable étale realization and étale cobordism |
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Authors: | Gereon Quick |
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Affiliation: | Mathematisches Institut, WWU Münster, Einsteinstr. 62, 48149 Münster, Germany |
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Abstract: | 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 A1-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. |
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Keywords: | 14F42 14F35 |
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