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arXiv 2402.062072024-02math.ACmath.AGmath.NT

棱柱克努斯定理

Prismatic Kunz's theorem

Institute of Science Tokyo（东京科学大学）；Proxima Technology Inc.（Proxima科技有限公司）

Ryo Ishizuka, Kei Nakazato

备注：: 31 pages; accepted in J.Algebra
DOI：: 10.1016/j.jalgebra.2026.01.010

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本文通过研究棱柱的正则性变形问题，证明了棱柱克努斯定理，扩展了经典克努斯定理到混合特征环的情形。

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在本文中，我们证明了

英文摘要：

In this paper, we prove "prismatic Kunz's theorem" which states that a complete Noetherian local ring $R$ of residue characteristic $p$ is a regular local ring if and only if the Frobenius lift on a prismatic complex of (a derived enhancement of) $R$ over a specific prism $(A, I)$ is faithfully flat. This generalizes classical Kunz's theorem from the perspective of extending the "Frobenius map" to mixed characteristic rings. Our approach involves studying the deformation problem of the "regularity" of prisms and demonstrating the faithful flatness of the structure map of the prismatic complex.

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