论文标题
$ q $ - 具有（$φ，γ$）的结构的元素结构
$q$-deformation with ($φ, Γ$) structure of the de Rham cohomology of the Legendre family of elliptic curves
论文作者
论文摘要
在60年代后期，B。DWORK研究了与经典的超小几何分化方程与参数$ \ left（\ frac {1} {2}，\ frac {1} {2} {2}; 1 \ right）$兼容的Frobenius结构。最近，P。Scholze猜想了任何$ \ Mathbb {Z} $ - 方案的存在$ Q $ -DE RHAM共同学组。在本文中，我们给出了一个与$ q $ - hyphemementional方程与参数$（q^{\ frac12}，q^{\ frac12}; q）兼容的frobenius结构。该结构提供了$（φ，γ）$ - 结构的$ q $ - $ \ MATHBB {Z} _p [[Q-1]] [[[Q-1]] [[[λ]] $ $ p $ - ad rham的共同体，具有Frobenius结构和连接。
In the late '60s, B. Dwork studied a Frobenius structure compatible with the classical hypergeometric differential equation with parameters $\left(\frac{1}{2},\frac{1}{2} ; 1 \right)$ by analyzing behavior of solutions of the differential equation under Frobenius transformation. Recently, P. Scholze conjectured the existence of $q$-de Rham cohomology groups for any $\mathbb{Z}$-scheme. In this paper, we give a Frobenius structure compatible with the $q$-hypergeometric differential equation with parameters $(q^{\frac12},q^{\frac12};q)$ by showing a $q$-analogue of some results of Dwork. This construction gives a $q$-deformation with $(φ,Γ)$-structure over $\mathbb{Z}_p[[q-1]][[λ]]$ of the de Rham cohomology of the $p$-adic Legendre family of elliptic curves which has Frobenius structure and connection.
