Thursday, August 28, 14:00, 7.527

Jiangwei Xue (Wuhan University), Conjugacy classes of
elements of finite orders in certain arithmetic subgroups.

Abstract:

Let k be a finite field of even degree over its prime
subfield F_{p}. By the theory of Galois descent, there is a bijection
between the isomorphism classes of superspecial abelian surfaces and the
set of conjugacy classes of elements of finite orders in GL_{2}(O),
where
O is a maximal order in the quaternion Q-algebra ramified only at p and
infinity. We explain the strategy of counting the latter set, which
reduces to classifying certain lattices over orders of semisimple
algebras. This is a joint work with Chia-Fu Yu and Tse-Chung Yang.