R202, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 202室)
Reduced Unit Groups of Maximal Orders of Denite Quaternion Algebras Over Real Quadratic Elds
Jiangwei Xue (
Wuhan University
)
Abstract
Let
be a totally definite quaternion algebra over a totally real field
, and
an
-order in
. The quotient
is a finite group, called the reduced unit group of
. Assume that
is real quadratic. We classify the reduced unit groups of all maximal orders, and count the number of conjugacy classes of maximal orders with a fixed reduced unit group for each possible non-cyclic group. When applied to the case
and
splitting at all finite places of
, this result produces the number of isomorphism classes of certain supersingular abelian surfaces with a specific reduced automorphism group within the isogeny class corresponding to the Weil numbers
. This is a joint work with Qun Li and Prof. Chia-Fu Yu.
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