论文标题
Bökstedt周期性的切片完善
A slice refinement of Bökstedt periodicity
论文作者
论文摘要
令$ r $为一个完美的环。 Hesselholt和Bhatt-Morrow-Scholze已确定了$ \ Mathrm {thh}（r; \ Mathbb z_p）$的nikov过滤：它均匀地集中在BökstedtGenerator $σ$上产生的bökstedtGenerator $σ$，clentalicalbökstedtecerticalof $ r = f = pp f = f = f = f = cl = f = f = f = f = f = f = f = f = f = f = c。我们在$ \ mathrm {thh}（r; \ mathbb z_p）$上研究了后尼科夫过滤， *常规切片过滤 *的均等概括。切片过滤再次集中在均匀度上，由$ RO（\ Mathbb t）$ - 分级类生成，可以松散地将其视为$σ$的 * norms *。这些切片可表示为$ ro（\ mathbb t）$ - 从Witt Mackey Foundor获得的Mackey Foundor的分级悬架。我们通过$ q $ factorials获得了一种过滤。一种可能具有独立关注的关键成分是切片过滤的山丘表征与Anschütz-le Bras'$ q $ - 赋予Legendre公式的信息之间的密切联系。
Let $R$ be a perfectoid ring. Hesselholt and Bhatt-Morrow-Scholze have identified the Postnikov filtration on $\mathrm{THH}(R;\mathbb Z_p)$: it is concentrated in even degrees, generated by powers of the Bökstedt generator $σ$, generalizing classical Bökstedt periodicity for $R=\mathbb F_p$. We study an equivariant generalization of the Postnikov filtration, the *regular slice filtration*, on $\mathrm{THH}(R;\mathbb Z_p)$. The slice filtration is again concentrated in even degrees, generated by $RO(\mathbb T)$-graded classes which can loosely be thought of as the *norms* of $σ$. The slices are expressible as $RO(\mathbb T)$-graded suspensions of Mackey functors obtained from the Witt Mackey functor. We obtain a sort of filtration by $q$-factorials. A key ingredient, which may be of independent interest, is a close connection between the Hill-Yarnall characterization of the slice filtration and Anschütz-le Bras' $q$-deformation of Legendre's formula.
