Is Infinite Dimensional

Lang, Jaclyn; Ludwig, Judith

doi:10.1017/s1474748020000201

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Tilting Untilting and Witt Vectors1

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2020

2022

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Cited by 4 publications

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“…is not finitely generated. In fact, A inf (F ) has infinite [37] and even uncountable [13] global dimension, and in general is not even coherent [30].…”

Section: Tilting Untilting and Witt Vectorsmentioning

confidence: 99%

Perfectoid Spaces: An Annotated Bibliography

Kedlaya

2022

Infosys Science Foundation Series

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This annotated bibliography was prepared as part of a five-lecture series at the summer school on perfectoid spaces held at the International Centre for Theoretical Sciences (ICTS), Bengaluru, September 9-13, 2019. It is not intended to be a freestanding reference, although we do include a few short proofs and some sketches of longer proofs; instead, I have attempted to give some complements to my Arizona Winter School 2017 lecture notes [28], which provide a far more complete version of the story.Throughout, fix a prime number p.

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“…is not finitely generated. In fact, A inf (F ) has infinite [37] and even uncountable [13] global dimension, and in general is not even coherent [30].…”

Section: Tilting Untilting and Witt Vectorsmentioning

confidence: 99%

Perfectoid Spaces: An Annotated Bibliography

Kedlaya

2022

Infosys Science Foundation Series

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Notes on the $$\mathbb A_{{\mathrm {inf}}}$$-Cohomology of Integral p-Adic Hodge Theory

Morrow¹

2020

Simons Symposia

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Some Ring-Theoretic Properties of $$\mathbf {A}_{{{\mathrm{inf}\,}}}$$

Kedlaya

2020

Simons Symposia

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The ring of Witt vectors over a perfect valuation ring of characteristic p, often denoted A inf , plays a pivotal role in p-adic Hodge theory; for instance, Bhatt-Morrow-Scholze have recently reinterpreted and refined the crystalline comparison isomorphism by relating it to a certain A inf -valued cohomology theory. We address some basic ring-theoretic questions about A inf , motivated by analogies with two-dimensional regular local rings. For example, we show that in most cases A inf , which is manifestly not noetherian, is also not coherent. On the other hand, it does have the property that vector bundles over the complement of the closed point in Spec A inf do extend uniquely over the puncture; moreover, a similar statement holds in Huber's category of adic spaces.

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Is Infinite Dimensional

Abstract: Given a perfect valuation ring $R$ of characteristic Show more

Cited by 4 publications

References 6 publications

Perfectoid Spaces: An Annotated Bibliography

Perfectoid Spaces: An Annotated Bibliography

Notes on the $$\mathbb A_{{\mathrm {inf}}}$$-Cohomology of Integral p-Adic Hodge Theory

Some Ring-Theoretic Properties of $$\mathbf {A}_{{{\mathrm{inf}\,}}}$$

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