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  • 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 Fp. 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.