تقرير
A general framework for tropical differential equations
| العنوان: | A general framework for tropical differential equations |
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| المؤلفون: | Giansiracusa, Jeffrey, Mereta, Stefano |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, Mathematics - Commutative Algebra, Mathematics - Rings and Algebras, Primary 14A20, Secondary 12H99, 13N99, 14T05, 14T99 |
| الوصف: | We construct a general framework for tropical differential equations based on idempotent semirings and an idempotent version of differential algebra. Over a differential ring equipped with a non-archimedean norm enhanced with additional differential information, we define tropicalization of differential equations and tropicalization of their solution sets. This framework includes rings of interest in the theory of p-adic differential equations: rings of convergent power series over a non-archimedean normed field. The tropicalization records the norms of the coefficients. This gives a significant refinement of Grigoriev's framework for tropical differential equations. We then prove a differential analogue of Payne's inverse limit theorem: the limit of all tropicalizations of a system of differential equations is isomorphic to a differential variant of the Berkovich analytification. Comment: 25 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2111.03925 |
| رقم الأكسشن: | edsarx.2111.03925 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |