# A non-archimedean definable Chow theorem

@article{Oswal2020AND, title={A non-archimedean definable Chow theorem}, author={Abhishek Oswal}, journal={arXiv: Algebraic Geometry}, year={2020} }

Peterzil and Starchenko have proved the following surprising generalization of Chow's theorem: A closed analytic subset of a complex algebraic variety that is definable in an o-minimal structure, is in fact an algebraic subset. In this paper, we prove a non-archimedean analogue of this result.

## References

SHOWING 1-10 OF 39 REFERENCES

### Variation de la dimension relative en géométrie analytique p-adique

- MathematicsCompositio Mathematica
- 2007

Abstract Let k be a complete, non-Archimedean valued field (the trivial absolute value is allowed) and let φ:X→Y be a morphism between two Berkovich k-analytic spaces; we show that, for any integer…

### Rigid subanalytic subsets of the line and the plane

- Mathematics
- 1996

Working over an algebraically closed, complete non-Archimedean non-trivially valued field, we show that any subanalytic subset of the line is semialgebraic and that any subanalytic subset of the…

### Spectral Theory and Analytic Geometry over Non-Archimedean Fields

- Mathematics
- 1990

The spectrum of a commutative Banach ring Affinoid spaces Analytic spaces Analytic curves Analytic groups and buildings The homotopy type of certain analytic spaces Spectral theory Perturbation…

### Model Theory with Applications to Algebra and Analysis: Complex analytic geometry in a nonstandard setting

- Mathematics
- 2008

Given an arbitrary o-minimal expansion of a real closed field R, we develop the basic theory of definable manifolds and definable analytic sets, with respect to the algebraic closure of R, along the…

### Tame Complex Analysis and o-minimality

- Mathematics
- 2011

We describe here a theory of holomorphic functions and analytic manifolds, restricted to the category of definable objects in an o-minimal structure which expands a real closed field R. In this…

### Algebraic Geometry and Arithmetic Curves

- Mathematics
- 2002

Introduction 1. Some topics in commutative algebra 2. General Properties of schemes 3. Morphisms and base change 4. Some local properties 5. Coherent sheaves and Cech cohmology 6. Sheaves of…

### Rigid subanalytic sets

- Mathematics
- 1994

Let K be an algebraically closed field endowed with a complete non-archimedean norm. Let f : Y → X be a map of K-affinoid varieties. In this paper we study the analytic structure of the image f(Y ) ⊂…

### Commutative Ring Theory

- Mathematics
- 1989

Preface Introduction Conventions and terminology 1. Commutative rings and modules 2. prime ideals 3. Properties of extension rings 4. Valuation rings 5. Dimension theory 6. Regular sequences 7.…