symmetric monoidal (∞,1)-category of spectra
A (complete) Archimedean valued field is a field equipped with an archimedean absolute value (and complete with respect to it).
A non-Archimedean valued field is one that is not, hence one whose norm satisfies the ultrametric triangle inequality.
One of Ostrowski's theorems says that for a field complete with respect to an absolute value either the absolute value is archimedean valued, in which case is either the field of real numbers or of complex numbers, or the absolute value is non-archimedean.
For a non-Archimedean valued field for some non-Archimedean absolute value one defines
its ring of integers to be
This is a local ring with maximal ideal
The residue field of is the quotient
Archimedean valued fields include
Non-Archimedean valued fields include
Last revised on December 13, 2023 at 02:50:21. See the history of this page for a list of all contributions to it.