LMFDB - Irreducible variety (reviewed)

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A variety defined over a field $F$ is irreducible if it is nonempty and cannot be decomposed as the union of two strictly smaller varieties over $F$ . It is geometrically irreducible if it remains irreducible when seen as a variety over the algebraic closure of $F$ .

Authors:

Bjorn Poonen
Andrew Sutherland
Nicolas Mascot

Knowl status:

Review status: reviewed
Last edited by Bjorn Poonen on 2022-03-24 16:12:41

Referred to by:

ag.dimension
g2c.locally_solvable

History: (expand/hide all)

2022-03-24 16:12:41 by Bjorn Poonen (Reviewed)
2019-05-12 10:00:30 by Andrew Sutherland (Reviewed)
2017-06-14 17:39:19 by Nicolas Mascot (Reviewed)

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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L-functions

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.