کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
403069 677044 2015 26 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Algorithms for Mumford curves
ترجمه فارسی عنوان
الگوریتم های منحنی مامورد
کلمات کلیدی
منحنی مامورد، هندسه گرمسیری
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر هوش مصنوعی
چکیده انگلیسی

Mumford showed that Schottky subgroups of PGL(2,K)PGL(2,K) give rise to certain curves, now called Mumford curves, over a non-archimedean field K. Such curves are foundational to subjects dealing with non-archimedean varieties, including Berkovich theory and tropical geometry. We develop and implement numerical algorithms for Mumford curves over the field of p-adic numbers. A crucial and difficult step is finding a good set of generators for a Schottky group, a problem solved in this paper. This result allows us to design and implement algorithms for tasks such as: approximating the period matrices of the Jacobians of Mumford curves; computing the Berkovich skeleta of their analytifications; and approximating points in canonical embeddings. We also discuss specific methods and future work for hyperelliptic Mumford curves.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Symbolic Computation - Volume 68, Part 2, May–June 2015, Pages 259–284
نویسندگان
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