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整数の微分とそれと両立する新たな多様体 II
http://hdl.handle.net/10935/5817
http://hdl.handle.net/10935/581788144194-5f47-412e-ba49-0cbdbca2db50
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
issn09132201v37pp101-109.pdf
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| アイテムタイプ | default_紀要論文 / Departmental Bulletin Paper(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2022-06-29 | |||||
| タイトル | ||||||
| タイトル | 整数の微分とそれと両立する新たな多様体 II | |||||
| 言語 | ja | |||||
| 言語 | ||||||
| 言語 | jpn | |||||
| キーワード | ||||||
| 言語 | ja | |||||
| 主題Scheme | Other | |||||
| 主題 | 整数 | |||||
| キーワード | ||||||
| 言語 | ja | |||||
| 主題Scheme | Other | |||||
| 主題 | 代数学 | |||||
| キーワード | ||||||
| 言語 | ja | |||||
| 主題Scheme | Other | |||||
| 主題 | 微分 | |||||
| 資源タイプ | ||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
| 資源タイプ | departmental bulletin paper | |||||
| その他（別言語等）のタイトル | ||||||
| その他のタイトル | Differentials of Integers on a New Manifold II | |||||
| 言語 | en | |||||
| 著者 |
角田,秀一郎
× 角田,秀一郎 |
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| 内容記述 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | This paper is a second paper concerning "Differentials of Integers."To study a compact complex manifold, an approach using differential geometry is known to be effective. Here we name few examples. The first one is Hodge theorem. In a classical proof of the theorem, we use Laplacian type differential equations. Next, we mention example by Yau. Yau proved existence of a Einstein Kaehler metric. To prove it, he solved a certain type of Monge-Ampere equations. The existence of a Hermitian Einstein metric on a stable vector bundle by Donaldson is another example. On these examples, we note that we solve differential equations related to metrics. They tell analytic structures of a manifold. Therefore it is natural to ask whether the solutions have better regularity or not. In the previous paper, we made differentials on integers, new manifolds where the differentials on integers and usual differentials on polynomials are compatible. Furthermore, we rewrite ordinary differential equations in terms of our new differentials which is meaningful on arithmetic manifolds. If we expect to have solutions, we extend functions. To do that, we need to consider a certain type of subharmonic functions which is written by regular functions in some sense. The type of subharmonic functions is extendable to both that of arithmetic manifolds and that of algebraic manifolds with positive characteristic. In this paper, we extend above theory to infinite value on the set of real numbers with absolute value less than equal to one. we provide a theory of a half to be parameter on the infinite point. In a same fashion of the previous paper, we define Wronskians and prove several properties of Wronskians. Furthermore, we define an equivalent notion of a canonical bundle on the algebraic geometry. Finally, we construct a new object that is similar to the projective line. The scheme of the ring of integers is realized as an possibly infinite cover of the object. | |||||
| 言語 | en | |||||
| 書誌情報 |
ja : 人間文化総合科学研究科年報 巻 37, p. 101-109, 発行日 2022-03-31 |
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| 出版者 | ||||||
| 出版者 | 奈良女子大学大学院人間文化総合科学研究科 | |||||
| 言語 | ja | |||||
| ISSN | ||||||
| 収録物識別子タイプ | PISSN | |||||
| 収録物識別子 | 0913-2201 | |||||
| 著者版フラグ | ||||||
| 出版タイプ | VoR | |||||
| 出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||
