论文标题
带支持的同胞的搬动引理
A moving lemma for cohomology with support
论文作者
论文摘要
对于具有支持的自然阶段的共同体理论（包括具有合适系数的典范或亲埃塔尔共同体），我们证明了同胞课程的移动引理，并支持平滑的准标记k-varieties，可以承认平滑的投射压缩（例如char（k）= 0）。这对此类k varieties和协同理论产生了以下后果：对Quillen，Bloch-ogus和Gabber的局部和全球概括，这是特征性零的Gersten猜想的有限级版本，以及对注射率属性的普遍性和编码1 purity for inorem for inorem for inoremology的普遍性。我们的结果表明，来自[SCH23]的精致未经塑造的共同体组是动机。
For a natural class of cohomology theories with support (including étale or pro-étale cohomology with suitable coefficients), we prove a moving lemma for cohomology classes with support on smooth quasi-projective k-varieties that admit a smooth projective compactification (e.g. if char(k)=0). This has the following consequences for such k-varieties and cohomology theories: a local and global generalization of the effacement theorem of Quillen, Bloch--Ogus, and Gabber, a finite level version of the Gersten conjecture in characteristic zero, and a generalization of the injectivity property and the codimension 1 purity theorem for étale cohomology. Our results imply that the refined unramified cohomology groups from [Sch23] are motivic.
