Places of algebraic function fields in arbitrary characteristic
By Franz-Viktor Kuhlmann. 2004
50 citations recorded by the source corpus.
We consider the Zariski space of all places of an algebraic function field F|K of arbitrary characteristic and investigate its structure by means of its patch topology. We show that certain sets of places with nice properties (e.g., prime divisors, places of maximal rank, zero-dimensional discrete places) lie dense in this topology. Further, we give several equivalent characterizations of fields that are large, in the sense of F. Pop's Annals paper Embedding problems over large fields. We also study the question whether a field K is existentially closed in an extension field L if L admits a K-rational place. In the appendix, we prove the fact that the Zariski space with the Zariski topology is quasi-compact and that it is a spectral space.
Subfields: Algebra and Number Theory, Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/1f73b55bc162ece71a40d26482999e54037fdd0d
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In Algebra and Number Theory
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Citations in the corpus
- Little survey on large fields - old & new (2014, background): “Kuhlmann [41] contains a detailed account of the relation between existentially closed field extensions, local uniformization à la Zariski, and large fields.”
- The algebra and model theory of tame valued fields (2013, methodology): “It was used in [22] in connection with the characterization of large fields.”