论文标题
混合特性和de rham-witt代数的分级环空间
Graded loopspaces in mixed characteristics and de Rham-Witt algebra
论文作者
论文摘要
该博士手稿的重点是研究带有Frobenius升降机的混合分级衍生方案的分级环空间构建变化。我们在衍生的堆栈上开发了一种衍生的Frobenius升降机理论，该理论是通勤环的三角洲结构的同型理论类似物。该分级环空间构建是针对派生方案的De Rham-Witt综合体定义的第一步。在这种情况下，“晶体圆”的作用给出了一个循环，该动作是拓扑圆的形式类似物，并赋予其自然的内态性，该内态由p乘以p。用这种语言，衍生的dieudonné综合体可以看作是具有晶体圆的作用的分级模块。
This PhD manuscript focuses on the study of a variation of the graded loop space construction for mixed graded derived schemes endowed with a Frobenius lift. We developed a theory of derived Frobenius lifts on a derived stack which are homotopy theoretic analogues of delta-structures for commutative rings. This graded loop space construction is the first step towards a definition of the de Rham-Witt complex for derived schemes. In this context, a loop is given by an action of the "crystalline circle", which is a formal analogue of the topological circle, endowed with its natural endomorphism given by multiplication by p. In this language, a derived Dieudonné complex can be seen as a graded module endowed with an action of the crystalline circle.
