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2 results

6 - Weil restriction for schemes and beyond
- By Lena Ji, Shizhang Li, Patrick McFaddin, Drew Moore, Matthew Stevenson
Edited by Pieter Belmans, Université du Luxembourg, Wei Ho, University of Michigan, Ann Arbor, Aise Johan de Jong, Columbia University, New York
Book:

Stacks Project Expository Collection

Published online:

06 October 2022

Print publication:

27 October 2022, pp 194-221
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Summary

The aim of this note is to discuss the Weil restriction of schemes and algebraic spaces, highlighting pathological phenomena that appear in the theory and are not widely known. It is shown that the Weil restriction of a locally finite algebraic space along a finite flat morphism is an algebraic space.

Nagata compactification for algebraic spaces
Part of
- Algebraic geometry: Foundations
- Birational geometry
Brian Conrad, Max Lieblich, Martin Olsson
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 11 / Issue 4 / October 2012

Published online by Cambridge University Press:

13 July 2012, pp. 747-814

Print publication:

October 2012
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We prove the Nagata compactification theorem for any separated map of finite type between quasi-compact and quasi-separated algebraic spaces, generalizing earlier results of Raoult. Along the way we also prove (and use) absolute noetherian approximation for such algebraic spaces, generalizing earlier results in the case of schemes.

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2 results

6 - Weil restriction for schemes and beyond

Summary

Nagata compactification for algebraic spaces