2 citations · 5 across the 7 of their papers we have counts for
10 papers
Semisimplicity, purity and Mumford-Tate conjecture for hyper-Kähler varieties
Kazuhiro Ito, Haitao Zou
We prove the Mumford-Tate conjecture in every degree for hyper-Kähler varieties over fields finitely generated over . The proof establishes semisimplicity of -adi…
Quasi--split primitive symplectic varieties in positive characteristic
Haitao Zou
Let be the good reduction of a projective hyperkähler variety of dimension . We prove that is quasi--split if and only if it is Frobenius split, equivalently if…
Monodromy rank and the semisimple Mumford-Tate conjecture for hyper-Kähler varieties
Zhichao Tang, Haitao Zou
We study the Mumford-Tate conjecture for hyper-Kähler varieties. We identify the Mumford-Tate group with a Levi factor of the connected total -adic monodromy group. It follow…
Arithmetic monodromy of hyper-Kähler varieties over -adic fields
Kazuhiro Ito, Tetsushi Ito, Teruhisa Koshikawa +2
In this paper, we study the -adic and -adic monodromy operators associated with hyper-Kähler varieties over -adic fields, in connection with Looijenga-Lunts-Verbitsky L…
Finiteness of pointed families of symplectic varieties: a geometric Shafarevich conjecture
Lie Fu, Zhiyuan Li, Teppei Takamatsu +1
We investigate in this paper the so-called pointed Shafarevich problem for families of primitive symplectic varieties. More precisely, for any fixed pointed curve and any…
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…
Unpolarized Shafarevich conjectures for hyper-Kähler varieties
Lie Fu, Zhiyuan Li, Haitao Zou
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 collection o…
Derived isogenies and isogenies for abelian surfaces
Zhiyuan Li, Haitao Zou
In this paper, we study the twisted Fourier-Mukai partners of abelian surfaces. Following the work of Huybrechts [doi:10.4171/CMH/465], we introduce the twisted derived equivalence…
A note on Fourier-Mukai partners of abelian varieties over positive characteristic fields
Zhiyuan Li, Haitao Zou
Over complex numbers, the Fourier-Mukai partners of abelian varieties are well-understood. A celebrated result is Orlov's derived Torelli theorem. In this note, we study the FM-par…
Supersingular O'Grady varieties of dimension six
Lie Fu, Zhiyuan Li, Haitao Zou
O'Grady constructed a 6-dimensional irreducible holomorphic symplectic variety by taking a crepant resolution of some moduli space of stable sheaves on an abelian surface. In this…