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arXiv · 2603.00559

On log crystalline higher direct image

Heng Du·Yong Suk Moon·Koji Shimizu
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Abstract

We define the big crystalline site for a log scheme and prove the basic properties. In particular, we show the boundedness, base change, and perfectness theorems for the crystalline higher direct image of quasi-coherent crystals between fine log schemes. We also introduce the big absolute crystalline sites and discuss the Frobenius isogeny property of the crystalline higher direct image of $F$-isocrystals.

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Heng Du, Yong Suk Moon, Koji Shimizu. 2026-02-28. On log crystalline higher direct image. https://arxiv.org/abs/2603.00559

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