Ehud Hrushovski is professor of mathematics at the Hebrew University of Jerusalem. He is the coauthor of Finite Structures with Few Types (Princeton) and Stable Domination and Independence in Algebraically Closed Valued Fields. Francois Loeser is professor of mathematics at Pierre-and-Marie-Curie University in Paris.

"A major achievement, both in rigid algebraic geometry, and as an application of model-theoretic and stability-theoretic methods to algebraic geometry."---Anand Pillay, MathSciNet

• *Frontmatter, pg. i*Contents, pg. v*1. Introduction, pg. 1*2. Preliminaries, pg. 8*3. The space v of stably dominated types, pg. 37*4. Definable compactness, pg. 57*5. A closer look at the stable completion, pg. 70*6. GAMMA-internal spaces, pg. 76*7. Curves, pg. 92*8. Strongly stably dominated points, pg. 104*9. Specializations and ACV2F, pg. 119*10. Continuity of homotopies, pg. 142*11. The main theorem, pg. 154*12. The smooth case, pg. 177*13. An equivalence of categories, pg. 183*14. Applications to the topology of Berkovich spaces, pg. 187*Bibliography, pg. 207*Index, pg. 211*List of notations, pg. 215

Ehud Hrushovski is professor of mathematics at the Hebrew University of Jerusalem. He is the coauthor of Finite Structures with Few Types (Princeton) and Stable Domination and Independence in Algebraically Closed Valued Fields. Francois Loeser is professor of mathematics at Pierre-and-Marie-Curie University in Paris.

"A major achievement, both in rigid algebraic geometry, and as an application of model-theoretic and stability-theoretic methods to algebraic geometry."---Anand Pillay, MathSciNet

• *Frontmatter, pg. i*Contents, pg. v*1. Introduction, pg. 1*2. Preliminaries, pg. 8*3. The space v of stably dominated types, pg. 37*4. Definable compactness, pg. 57*5. A closer look at the stable completion, pg. 70*6. GAMMA-internal spaces, pg. 76*7. Curves, pg. 92*8. Strongly stably dominated points, pg. 104*9. Specializations and ACV2F, pg. 119*10. Continuity of homotopies, pg. 142*11. The main theorem, pg. 154*12. The smooth case, pg. 177*13. An equivalence of categories, pg. 183*14. Applications to the topology of Berkovich spaces, pg. 187*Bibliography, pg. 207*Index, pg. 211*List of notations, pg. 215

Ehud Hrushovski is professor of mathematics at the Hebrew University of Jerusalem. He is the coauthor of Finite Structures with Few Types (Princeton) and Stable Domination and Independence in Algebraically Closed Valued Fields. Francois Loeser is professor of mathematics at Pierre-and-Marie-Curie University in Paris.

"A major achievement, both in rigid algebraic geometry, and as an application of model-theoretic and stability-theoretic methods to algebraic geometry."---Anand Pillay, MathSciNet

• *Frontmatter, pg. i*Contents, pg. v*1. Introduction, pg. 1*2. Preliminaries, pg. 8*3. The space v of stably dominated types, pg. 37*4. Definable compactness, pg. 57*5. A closer look at the stable completion, pg. 70*6. GAMMA-internal spaces, pg. 76*7. Curves, pg. 92*8. Strongly stably dominated points, pg. 104*9. Specializations and ACV2F, pg. 119*10. Continuity of homotopies, pg. 142*11. The main theorem, pg. 154*12. The smooth case, pg. 177*13. An equivalence of categories, pg. 183*14. Applications to the topology of Berkovich spaces, pg. 187*Bibliography, pg. 207*Index, pg. 211*List of notations, pg. 215