Unit groups of maximal orders in totally definite quaternion algebras over real quadratic fields
| Autor: | Chia-Fu Yu, Qun Li, Jiangwei Xue |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Endomorphism
Mathematics - Number Theory Group (mathematics) Applied Mathematics General Mathematics 010102 general mathematics Center (category theory) Automorphism 01 natural sciences Class number formula Combinatorics Conjugacy class FOS: Mathematics 11R52 11R29 11G10 Number Theory (math.NT) 0101 mathematics Abelian group Unit (ring theory) Mathematics |
| Popis: | We study a form of refined class number formula (resp. type number formula) for maximal orders in totally definite quaternion algebras over real quadratic fields, by taking into consideration the automorphism groups of right ideal classes (resp. unit groups of maximal orders). For each finite noncyclic group $G$, we give an explicit formula for the number of conjugacy classes of maximal orders whose unit groups modulo center are isomorphic to $G$, and write down a representative for each conjugacy class. This leads to a complete recipe (even explicit formulas in special cases) for the refined class number formula for all finite groups. As an application, we prove the existence of superspecial abelian surfaces whose endomorphism algebras coincide with $\mathbb{Q}(\sqrt{p})$ in all positive characteristic $p\not\equiv 1\pmod{24}$. 54 pages, exposition greatly improved, results unchanged |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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