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Results tagged with fields
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user 3545
Fields as algebraic objects. For vector and tensor fields, use eg. [dg.differential-geometry]. For physical fields, use eg. [mp.mathematical-physics] or [quantum-field-theory].
11
votes
If a field extension gives affine space, was it already affine space?
First, since the OP is interested in Bruhat cells in flag varieties over nonsplit groups (over perfect fields), I think the question is probably unnecessary. … So, I doubt that twists of affine spaces have any place in studying Bruhat cells for nonsplit groups reductive groups over perfect fields. …
- 13.3k
18
votes
Accepted
Are there as many real-closed fields of a given cardinality as I think there are?
I believe that Shelah's theorem, from his 1971 paper "The number of non-isomorphic models of an unstable first-order theory" (Israel J. of Math) answers your question about real closed fields in the positive … To answer the question on real closed fields specifically (and somewhat cautiously since I'm not a model-theorist):
The theory of real closed fields is a complete first order theory, with countable language …
- 13.3k