Completeness and compactness for varieties over a local field

Oliver Lorscheid

doi:10.1007/s00013-006-1987-0

Completeness and compactness for varieties over a local field

Oliver Lorscheid^*

^*Corresponding author for this work

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Abstract

This paper shows that for a local field K, a subfield k ⊂ K and a variety X over k, X is complete if and only if for every finite field extension Kʹ | K, the set X(Kʹ) is compact in its strong topology.

Original language	English
Pages (from-to)	344-348
Number of pages	5
Journal	Archiv der mathematik
Volume	88
DOIs	https://doi.org/10.1007/s00013-006-1987-0
Publication status	Published - 2007
Externally published	Yes

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title = "Completeness and compactness for varieties over a local field",

abstract = "This paper shows that for a local field K, a subfield k ⊂ K and a variety X over k, X is complete if and only if for every finite field extension Kʹ | K, the set X(Kʹ) is compact in its strong topology.",

author = "Oliver Lorscheid",

year = "2007",

doi = "10.1007/s00013-006-1987-0",

language = "English",

volume = "88",

pages = "344--348",

journal = "Archiv der mathematik",

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PY - 2007

Y1 - 2007

N2 - This paper shows that for a local field K, a subfield k ⊂ K and a variety X over k, X is complete if and only if for every finite field extension Kʹ | K, the set X(Kʹ) is compact in its strong topology.

AB - This paper shows that for a local field K, a subfield k ⊂ K and a variety X over k, X is complete if and only if for every finite field extension Kʹ | K, the set X(Kʹ) is compact in its strong topology.

U2 - 10.1007/s00013-006-1987-0

DO - 10.1007/s00013-006-1987-0

M3 - Article

SN - 0003-889X

VL - 88

SP - 344

EP - 348

JO - Archiv der mathematik

JF - Archiv der mathematik

ER -

Completeness and compactness for varieties over a local field

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