The Ă©tale homotopy type of varieties over $\textbf {R}$
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- by David A. Cox PDF
- Proc. Amer. Math. Soc. 76 (1979), 17-22 Request permission
Abstract:
For a variety X over ${\text {Spec}}({\mathbf {R}})$, the Ă©tale homotopy type of X is computed in terms of the action of complex conjugation on the complex points $X({\mathbf {C}})$. This enables one to show that $X({\mathbf {R}}) \ne \emptyset$ is equivalent to various conditions on the Ă©tale cohomology of X, and, when X is a smooth, geometrically connected, proper curve over ${\text {Spec}}({\mathbf {R}})$, to compute the Ă©tale cohomology. Finally, there is a negative result, showing that Ă©tale cohomology cannot be used to compute the topological degree of a mapping germ $f:({{\mathbf {R}}^n},0) \to ({{\mathbf {R}}^n},0)$ .References
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Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 76 (1979), 17-22
- MSC: Primary 14F20
- DOI: https://doi.org/10.1090/S0002-9939-1979-0534381-4
- MathSciNet review: 534381