## 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.

### MSC:

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

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