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 GL₂(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.