Algebraic geometry in mixed characteristic

Bhatt, Bhargav

doi:10.48550/arxiv.2112.12010

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2022

2024

Publication Types

Select...

Article1

Other1

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(2 citation statements)

References 182 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Part of their work is reproved or generalized by Du and Liu [DL23], Wu [Wu21], and Min and Wang [MW21]. For other works on the prismatic site, we refer the reader to the recent survey [Bha21].…”

Section: Introductionmentioning

confidence: 99%

Completed prismatic F-crystals and crystalline Z_p-local systems

Du,

Liu,

Moon

et al. 2024

Compositio Math.

View full text Add to dashboard Cite

We introduce the notion of completed $F$ -crystals on the absolute prismatic site of a smooth $p$ -adic formal scheme. We define a functor from the category of completed prismatic $F$ -crystals to that of crystalline étale $\mathbf {Z}_p$ -local systems on the generic fiber of the formal scheme and show that it gives an equivalence of categories. This generalizes the work of Bhatt and Scholze, which treats the case of a mixed characteristic complete discrete valuation ring with perfect residue field.

show abstract

Section: Introductionmentioning

confidence: 99%

Completed prismatic F-crystals and crystalline Z_p-local systems

Du,

Liu,

Moon

et al. 2024

Compositio Math.

View full text Add to dashboard Cite

show abstract

“…Part of their work is reproved or generalized by Du-Liu [17], Wu [48], and Min-Wang [34]. For other works on the prismatic site, we refer the reader to a recent survey [4].…”

mentioning

confidence: 99%

Completed prismatic $F$-crystals and crystalline $\mathbf{Z}_p$-local systems

Du¹,

Liu²,

Moon³

et al. 2022

Preprint

View full text Add to dashboard Cite

We introduce the notion of completed F -crystals on the absolute prismatic site of a smooth p-adic formal scheme. We define a functor from the category of completed prismatic F -crystals to that of crystalline étale Z p -local systems on the generic fiber of the formal scheme and show that it gives an equivalence of categories. This generalizes the work of Bhatt and Scholze, which treats the case of a complete discrete valuation ring with perfect residue field.

show abstract

Algebraic geometry in mixed characteristic

Abstract: Fix a prime number p. We report on some recent developments in algebraic geometry (broadly construed) over p-adically complete commutative rings. These developments include foundational advances within the subject as well as external applications.

Cited by 2 publications

References 182 publications

Completed prismatic F-crystals and crystalline Z_p-local systems

Completed prismatic F-crystals and crystalline Z_p-local systems

Completed prismatic $F$-crystals and crystalline $\mathbf{Z}_p$-local systems

Contact Info

Product

Resources

About

Algebraic geometry in mixed characteristic

Abstract: Fix a prime number p. We report on some recent developments in algebraic geometry (broadly construed) over p-adically complete commutative rings. These developments include foundational advances within the subject as well as external applications.

Cited by 2 publications

References 182 publications

Completed prismatic F-crystals and crystalline Zp-local systems

Completed prismatic F-crystals and crystalline Zp-local systems

Completed prismatic $F$-crystals and crystalline $\mathbf{Z}_p$-local systems

Contact Info

Product

Resources

About

Completed prismatic F-crystals and crystalline Z_p-local systems

Completed prismatic F-crystals and crystalline Z_p-local systems