2 citations · 4 across the 10 of their papers we have counts for
10 papers
Topological reconstruction theorems over uncountable algebraically closed fields
Benjamin Castle, Ronan O'Gorman
Working over uncountable algebraically closed fields, we extend the theorems of Kollár-Lieblich-Olsson-Sawin on reconstructing varieties from their Zariski topological spaces. In p…
A curve and its abstract generalized Jacobian
Benjamin Castle, Ishai Dan-Cohen, Assaf Hasson
To a smooth proper curve over a field equipped with a -point and an effective divisor coprime to , one may associate the abstract group $J_{\mathfra…
Topologically 1-based T-minimal Structures
Benjamin Castle, Assaf Hasson, Will Johnson
We prove group existence and structure theorems in a general setting of tame topological theories. More precisely, we identify a linear/non-linear dividing line -- called topologic…
Reconstructing Abelian Varieties via Model Theory
Benjamin Castle, Assaf Hasson
In 2012, Zilber used model-theoretic techniques to show that a curve of high genus over an algebraically closed field is determined by its Jacobian (viewed only as an abstract grou…
Strongly Minimal Relics of T-convex Fields
Benjamin Castle, Assaf Hasson
Generalizing previous work on algebraically closed valued fields (ACVF) and o-minimal fields, we study strongly minimal relics of real closed valued fields (RCVF), and more general…
The O-minimal Zilber Conjecture in Higher Dimensions
Benjamin Castle
We prove the higher dimensional case of the o-minimal variant of Zilber's Restricted Trichotomy Conjecture. More precisely, let be an o-minimal expansion of a real clo…
Zilber's Trichotomy in Hausdorff Geometric Structures
Benjamin Castle, Assaf Hasson, Jinhe Ye
We give a new axiomatic treatment of the Zilber trichotomy, and use it to complete the proof of the trichotomy for relics of algebraically closed fields, i.e., reducts of the ACF-i…
Model Theory of Complex Numbers with Polynomial Functions
Benjamin Castle, Chieu-Minh Tran
Let be the set of complex numbers, and let be a collection of complex polynomial maps in several variables. Assuming at least one depends…
Very ampleness in strongly minimal sets
Benjamin Castle, Assaf Hasson
Inspired by very ampleness of Zariski Geometries, we introduce and study the notion of a very ample family of plane curves in any strongly minimal set, and the corresponding notion…
Restricted Trichotomy in Characteristic Zero
Benjamin Castle
We prove the characteristic zero case of Zilber's Restricted Trichotomy Conjecture. That is, we show that if is any non-locally modular strongly minimal structure inte…