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math.AG2026
Unpolarized Shafarevich conjectures for hyper-Kähler varieties
Lie Fu, Zhiyuan Li, Teppei Takamatsu +1
The Shafarevich conjecture/problem is about the finiteness of isomorphism classes of a family of varieties defined over a number field with good reduction outside a finite collecti…
math.AG2025
Algebraic cycles on Gushel-Mukai varieties
Lie Fu, Ben Moonen
We study algebraic cycles on complex Gushel-Mukai (GM) varieties. We prove the generalised Hodge conjecture, the (motivated) Mumford-Tate conjecture, and the generalised Tate conje…
math.AG2024
The Tate Conjecture for even dimensional Gushel-Mukai varieties in characteristic
Lie Fu, Ben Moonen
We study Gushel-Mukai (GM) varieties of dimension 4 or 6 in characteristic . Our main result is the Tate conjecture for all such varieties over finitely generated fields of char…