Hilbert's Theorem 90 and algebraic spaces

Stefan Schroeer

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arXiv · math/0110243

Hilbert's Theorem 90 and algebraic spaces

Stefan Schroeer

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Abstract

In modern form, Hilbert's Theorem 90 tells us that R^1f_*(G_m)=0, where f is the canonical map between the etale site and the Zariski site of a scheme X. I construct examples showing that the corresponding statement for algebraic spaces does not hold. The first example is a nonseparated smooth 1-dimensional bug-eyed cover in Kollar's sense. The second example is a nonnormal proper algebraic space obtained by identifying points on suitable nonprojective smooth proper schemes.

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BibTeX RIS

Stefan Schroeer. 2001-10-22. Hilbert's Theorem 90 and algebraic spaces. https://arxiv.org/abs/math/0110243

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