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arxiv: 0810.0215 · v1 · submitted 2008-10-01 · 🧮 math.AC

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The root closure of a ring of mixed characteristic

Paul C. Roberts
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classification 🧮 math.AC
keywords closureringcharacteristicmixedpropertiesringscloseddefine
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We define a closure operation for rings of mixed characteristic and verify that the closure is a ring. We then show that this closure produces a ring with good properties with respect to its Fontaine ring and give an example to show that rings that are not closed in this sense do not satisfy these properties.

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  1. Algebraization of absolute perfectoidization via section rings

    math.AG 2026-04 unverdicted novelty 7.0

    A graded absolute perfectoidization is built for G-graded adic rings, with the key result that the absolute perfectoidization of the structure sheaf on projective-type formal schemes algebraizes.