Dimension theory and parameterized normalization for \(D\)-semianalytic sets over non-Archimedean fields. (English) Zbl 1119.03028

The author develops a dimension theory for \(D\)-semianalytic sets over an arbitrary non-Archimedean complete field. The equivalence of several notions of dimension and a theorem on additivity of dimensions of projections and fibers in characteristic \(0\) are proved. To compare the geometric dimension of a \(D\)-semianalytic set with the restricted dimension of the associated quasi-affinoid algebras, the author proves a difficult normalization lemma which is very useful for applications. Some results in positive characteristic are also obtained under some additional assumptions.


03C60 Model-theoretic algebra
12L12 Model theory of fields
12J25 Non-Archimedean valued fields
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