8 papers
A note on uniform finiteness in weakly o-minimal theories
Yatir Halevi, Assaf Hasson, Ya'acov Peterzil
For an -saturated weakly o-minimal expansion of an ordered group , it is shown that has uniform finiteness if and only if the colle…
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…
Semisimple groups interpretable in various valued fields
Yatir Halevi, Assaf Hasson, Ya'acov Peterzil
We study infinite groups interpretable in power bounded -convex, -minimal or -adically closed fields. We show that if is an interpretable definably semisimple group (i…
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…