AI 中文总结
研究代数空间有限表示满射在拓扑织构中的可降性准则，应用此准则证明有理动机层等满足v - 下降，并为阿廷层的恰当DM态射构造‘遗忘支撑’同构$f_! \simeq f_*$。
AI 中文摘要
我们证明了代数空间的有限表示满射在拓扑织构中可降的一个准则。我们应用此准则表明有理动机层满足v - 下降，对于具有一致有界平展上同调维数的诺特有限维概型上的平展动机谱也是如此。我们还在有理动机层中为阿廷层的恰当DM态射构造了“遗忘支撑”同构$f_! \simeq f_*$。
英文摘要
We prove a criterion for a finitely presented surjection of algebraic spaces to be descendable in a topological weave. We apply this to show that étale motivic spectra satisfy $h$-descent on noetherian finite-dimensional schemes with residue fields of uniformly bounded étale cohomological dimension. We also show that rational motivic cohomology satisfies arc-descent in weights $\le 1$, and we construct the ``forgetting supports'' isomorphism $f_! \simeq f_*$ for a proper DM-type morphism of Artin stacks, in rational motivic sheaves.
Comments27 pages. v2: removed the incorrect Thm. 2.14, added §3.2 on v- and arc-descent of rational motivic cohomology
