تقرير
Supersingular abelian surfaces and Eichler class number formula
| العنوان: | Supersingular abelian surfaces and Eichler class number formula |
|---|---|
| المؤلفون: | Xue, Jiangwei, Yang, Tse-Chung, Yu, Chia-Fu |
| سنة النشر: | 2014 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 11R52, 11G10 |
| الوصف: | Let $F$ be a totally real field with ring of integers $O_F$, and $D$ be a totally definite quaternion algebra over $F$. A well-known formula established by Eichler and then extended by K\"orner computes the class number of any $O_F$-order in $D$. In this paper we generalize the Eichler class number formula so that it works for arbitrary $\mathbb{Z}$-orders in $D$. The motivation is to count the isomorphism classes of supersingular abelian surfaces in a simple isogeny class over a prime finite field $\mathbb{F}_p$. We give explicit formulas for the number of these isomorphism classes for all primes $p$. Comment: 29 pages, 3 numerical tables, shortened revised version with same results, Sections 7-9 of v2 are removed |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1404.2978 |
| رقم الأكسشن: | edsarx.1404.2978 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |