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- W4297687145 abstract "In 1969 Artin and Mazur defined the 'etale homotopy type of an algebraic variety cite{AMa69}. In this paper we define various obstructions to the local-global principle on a variety $X$ over a global field using the 'etale homotopy type of $X$ and the concept of homotopy fixed points. We investigate relations between those homotopy obstructions and connect them to various known obstructions such as the Brauer -Manin obstruction, the 'etale-Brauer obstruction and finite descent obstructions. This gives a reinterpretation of known arithmetic obstructions in terms of homotopy theory." @default.
- W4297687145 created "2022-09-30" @default.
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- W4297687145 date "2010-02-06" @default.
- W4297687145 modified "2023-10-01" @default.
- W4297687145 title "The '{E}tale Homotopy Type and Obstructions to the Local-Global Principle" @default.
- W4297687145 doi "https://doi.org/10.48550/arxiv.1002.1423" @default.
- W4297687145 hasPublicationYear "2010" @default.
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