On Counting Certain Abelian Varieties Over Finite Fields
| العنوان: | On Counting Certain Abelian Varieties Over Finite Fields |
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| المؤلفون: | Chia-Fu Yu, Jiangwei Xue |
| المصدر: | Acta Mathematica Sinica, English Series. 37:205-228 |
| بيانات النشر: | Springer Science and Business Media LLC, 2020. |
| سنة النشر: | 2020 |
| مصطلحات موضوعية: | Isogeny, Pure mathematics, Class (set theory), Current (mathematics), Mathematics - Number Theory, Series (mathematics), Applied Mathematics, General Mathematics, 010102 general mathematics, 01 natural sciences, Connection (mathematics), Finite field, Simple (abstract algebra), 0103 physical sciences, FOS: Mathematics, Number Theory (math.NT), 010307 mathematical physics, 0101 mathematics, Abelian group, Mathematics |
| الوصف: | This paper contains two parts toward studying abelian varieties from the classification point of view. In a series of papers, the current authors and T.-C. Yang obtain explicit formulas for the numbers of superspecial abelian surfaces over finite fields. In this paper, we give an explicit formula for the size of the isogeny class of simple abelian surfaces with real Weil number $\sqrt{q}$. This establishes a key step that one may extend our previous explicit calculations of superspecial abelian surfaces to those of supersingular abelian surfaces.The second part is to introduce the notion of genera and ideal complexes of abelian varieties with additional structures in a general setting. The purpose is to generalize the results of Yu on abelian varieties with additional structures to similitude classes, which establishes more results on the connection between geometrically defined and arithmetically defined masses for further investigation. Comment: 23 pages. Section 5.4 corrected |
| تدمد: | 1439-7617 1439-8516 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::56a71eee808483a48d752a438d7daf48 https://doi.org/10.1007/s10114-020-8415-4 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....56a71eee808483a48d752a438d7daf48 |
| قاعدة البيانات: | OpenAIRE |
Find this article in full text from Springer Verlag. | تدمد: | 14397617 14398516 |
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