Algebraic theory of formal regular-singular connections with parameters
| Autor: | Hai, Phùng Hô, Santos, João Pedro dos, Tâm, Pham Thanh |
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| Rok vydání: | 2021 |
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| Druh dokumentu: | Working Paper |
| Popis: | This paper is divided into two parts. The first is a review, through categorical lenses, of the classical theory of regular-singular differential systems over $C((x))$ and $\mathbb P^1_C\smallsetminus\{0,\infty\}$, where $C$ is algebraically closed and of characteristic zero. It aims at reading the existing classification results as an equivalence between regular-singular systems and representations of the group $\mathbb Z$. In the second part, we deal with regular-singular connections over $R((x))$ and $\mathbb P_R^1\smallsetminus\{0,\infty\}$, where $R=C[[t_1,\ldots,t_r]]/I$. The picture we offer shows that regular-singular connections are equivalent to representations of $\mathbb Z$, now over $R$. Comment: To appear in Rend. Semin. Mat. Univ. Padova |
| Databáze: | arXiv |
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