发表机构
UC Santa Cruz（加州大学圣克鲁兹分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了 Serre-Grothendieck 有限性定理的逆定理，通过导出推前与完美复形扭转后的伪凝聚性，给出了真态射的新刻画。
AI 中文摘要
我们证明了 Serre-Grothendieck 有限性定理的逆定理，该定理最初由 Lipman 提出，针对凝聚层的上同调。此结果将真态射刻画为那些其导出推前保持伪凝聚复形的态射。尽管导出推前不反映伪凝聚性，我们证明它在与所有完美复形扭转后确实反映。这为真态射提供了新的刻画。
英文摘要
We prove the converse of the Serre-Grothendieck finiteness theorem for the cohomology of coherent sheaves, originally due to Lipman. This result characterizes proper morphisms as those morphisms whose derived pushforward preserves pseudo-coherent complexes. Although the derived pushforward does not reflect pseudo-coherence, we prove that it does after twisting by all perfect complexes. This provides a new characterization of properness.
Comments15 pages
