Completeness and compactness for varieties over a local field |
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Authors: | Oliver Lorscheid |
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Institution: | (1) Department of Mathematics, Utrecht University, Budapestlaan 6, NL-3584 CD Utrecht, The Netherlands |
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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.
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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Keywords: | Primary 11G25 Secondary 14A10 |
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