标题： 一种在光滑且$\mathbb{Z}$-挠自由情况下的相对德雷克尔-维特复形的几何方法 显示英文标题

标题： A geometric approach to the relative de Rham-Witt complex in the smooth, $\mathbb{Z}$-torsion free case

摘要： 设$X$为一个在有限生成的平坦$\mathbb{Z}$-、$\mathbb{Z}_{(p)}$- 或$\mathbb{Z}_p$-代数$R$上的光滑概形。 在有限截断集$S$上求值，相对德罗姆-维特复形$W_S\Omega_{X/R}^{\bullet}$是德罗姆复形$\Omega^{\bullet}_{W_S(X)/W_S(R)}$的商，可以通过显式的但复杂的关系在仿射局部计算。在本文中我们证明，$W_S\Omega_{X/R}^{\bullet}$是通常的德罗姆复形$\Omega^{\bullet}_{W_S(X)/W_S(R)}$在奇异概形$W_S(X)$上的无挠商。这一结果是通过与奇异流形理论中德罗姆复形类似修改的比较提出的。 显示英文摘要

摘要： Let $X$ be a smooth scheme over a finitely generated flat $\mathbb{Z}$-, $\mathbb{Z}_{(p)}$- or $\mathbb{Z}_p$-algebra $R$. Evaluated at finite truncation sets $S$, the relative de Rham-Witt complex $W_S\Omega_{X/R}^{\bullet}$ is a quotient of the de Rham complex $\Omega^{\bullet}_{W_S(X)/W_S(R)}$, which can be computed affine locally via explicit, but complicated relations. In this paper we prove that $W_S\Omega_{X/R}^{\bullet}$ is the torsionless quotient of the usual de Rham complex $\Omega^{\bullet}_{W_S(X)/W_S(R)}$ on the singular scheme $W_S(X)$. This result was suggested by comparison with a similar modification of the de Rham complex in the theory of singular varieties.