Galois descent criteria

J. F. Jardine

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arXiv · 1906.06292

Galois descent criteria

J. F. Jardine

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Abstract

This paper gives an introduction to homotopy descent, and its applications in algebraic $K$-theory computations for fields. On the \'etale site of a field, a fibrant model of a simplicial presheaf can be constructed from naive Galois cohomological objects given by homotopy fixed point constructions, but only up to pro-equivalence. The homotopy fixed point spaces define finite Galois descent for simplicial presheaves (and their relatives) over a field, but a pro-categorical construction is a necessary second step for passage from finite descent conditions to full homotopy descent in a Galois cohomological setting.

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BibTeX RIS

J. F. Jardine. 2019-06-14. Galois descent criteria. https://arxiv.org/abs/1906.06292

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