论文标题
半最终类别类别III：模块化函数变形的WITT向量
Semi-galois Categories III: Witt vectors by deformations of modular functions
论文作者
论文摘要
基于我们以前关于克里斯托尔定理的算术类似物的工作，本文更详细地研究了lambda-ring $ e_k = k \ otimes w_ {o_k}^a（o_ {\ bar {k}}）$ nimumb witt vectors for number firem firmumb fields $ k $ k $ k $ k $。首先开发有关$ e_k $的一般结果，当$ k $是一个虚构的二次字段时，我们将它们应用于情况。 The main results include the "modularity theorem" for algebraic Witt vectors, which claims that certain deformation families $f: M_2(\widehat{\mathbb{Z}}) \times \mathfrak{H} \rightarrow \mathbb{C}$ of modular functions of finite level always define algebraic Witt vectors $ \ wideHat {f} $以其特殊价值观，相反，以这种方式实现了e_k $中的每个代数witt vector $ξ\，也就是说，$ξ= \ widehat {f} {f} {f} $ f：m_2（\ wideHat {\ wideHat {\ mathbb {z} Z}}} \ Mathbb {C} $。这给出了对想象中的二次字段$ k $的lambda-ring $ e_k $的明确描述，该$ k $表示为身份$ e_k = m_k = m_k $ rombda-ring $ e_k $和$ k $ k $ -k $ -algebra $ algebra $ m_k $ m_k $ m_k $ m_k $ modular vectors $ \ fidehat $ \ fidehat f fiphat f f f f i f f i f} $。
Based on our previous work on an arithmetic analogue of Christol's theorem, this paper studies in more detail the structure of the lambda-ring $E_K = K \otimes W_{O_K}^a (O_{\bar{K}})$ of algebraic Witt vectors for number fields $K$. First developing general results concerning $E_K$, we apply them to the case when $K$ is an imaginary quadratic field. The main results include the "modularity theorem" for algebraic Witt vectors, which claims that certain deformation families $f: M_2(\widehat{\mathbb{Z}}) \times \mathfrak{H} \rightarrow \mathbb{C}$ of modular functions of finite level always define algebraic Witt vectors $\widehat{f}$ by their special values, and conversely, every algebraic Witt vector $ξ\in E_K$ is realized in this way, that is, $ξ= \widehat{f}$ for some deformation family $f: M_2(\widehat{\mathbb{Z}}) \times \mathfrak{H} \rightarrow \mathbb{C}$. This gives a rather explicit description of the lambda-ring $E_K$ for imaginary quadratic fields $K$, which is stated as the identity $E_K=M_K$ between the lambda-ring $E_K$ and the $K$-algebra $M_K$ of modular vectors $\widehat{f}$.
