From the 1 of 7 linked papers with an AI index.
7 papers
Topological reconstruction theorems over uncountable algebraically closed fields
Benjamin Castle, Ronan O'Gorman
The paper extends reconstruction theorems that recover algebraic varieties from their Zariski topological spaces to arbitrary quasi‑projective varieties over uncountable algebraica…
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…
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…
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…