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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.
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The author likes to thank Florian Pop, Jakob Stix, Stefan Wewers, Gunther Cornelissen and his own parents for their support.
Received: 13 April 2006
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Lorscheid, O. Completeness and compactness for varieties over a local field. Arch. Math. 88, 344–348 (2007). https://doi.org/10.1007/s00013-006-1987-0
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DOI: https://doi.org/10.1007/s00013-006-1987-0