Derived invariants from topological Hochschild homology

Benjamin Antieau; Daniel Bragg

doi:10.14231/AG-2022-011

Derived invariants from topological Hochschild homology

Benjamin Antieau^*, Daniel Bragg

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We consider derived invariants of varieties in positive characteristic arising from topological Hochschild homology. Using theory developed by Ekedahl and Illusie-Raynaud in their study of the slope spectral sequence, we examine the behavior under derived equivalences of various p-adic quantities related to Hodge-Witt and crystalline cohomology groups, including slope numbers, domino numbers, and Hodge-Witt numbers.

Original language	English (US)
Pages (from-to)	364-399
Number of pages	36
Journal	Algebraic Geometry
Volume	9
Issue number	3
DOIs	https://doi.org/10.14231/AG-2022-011
State	Published - May 2022

Keywords

Derived equivalence
Dominoes
Hodge numbers
The de rham-witt complex

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

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10.14231/AG-2022-011

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title = "Derived invariants from topological Hochschild homology",

abstract = "We consider derived invariants of varieties in positive characteristic arising from topological Hochschild homology. Using theory developed by Ekedahl and Illusie-Raynaud in their study of the slope spectral sequence, we examine the behavior under derived equivalences of various p-adic quantities related to Hodge-Witt and crystalline cohomology groups, including slope numbers, domino numbers, and Hodge-Witt numbers.",

keywords = "Derived equivalence, Dominoes, Hodge numbers, The de rham-witt complex",

author = "Benjamin Antieau and Daniel Bragg",

note = "Funding Information: The first author was supported by NSF Grant DMS-1552766. The second author was partially supported by NSF RTG grant DMS-1646385 and by NSF postdoctoral fellowship DMS-1902875. Both authors were supported by the National Science Foundation under Grant DMS-1440140 while in residence at the Mathematical Sciences Research Institute in Berkeley, California during the Spring 2019 semester. Publisher Copyright: {\textcopyright} Foundation Compositio Mathematica 2022",

year = "2022",

month = may,

doi = "10.14231/AG-2022-011",

language = "English (US)",

volume = "9",

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publisher = "European Mathematical Society Publishing House",

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T1 - Derived invariants from topological Hochschild homology

AU - Antieau, Benjamin

AU - Bragg, Daniel

N1 - Funding Information: The first author was supported by NSF Grant DMS-1552766. The second author was partially supported by NSF RTG grant DMS-1646385 and by NSF postdoctoral fellowship DMS-1902875. Both authors were supported by the National Science Foundation under Grant DMS-1440140 while in residence at the Mathematical Sciences Research Institute in Berkeley, California during the Spring 2019 semester. Publisher Copyright: © Foundation Compositio Mathematica 2022

PY - 2022/5

Y1 - 2022/5

N2 - We consider derived invariants of varieties in positive characteristic arising from topological Hochschild homology. Using theory developed by Ekedahl and Illusie-Raynaud in their study of the slope spectral sequence, we examine the behavior under derived equivalences of various p-adic quantities related to Hodge-Witt and crystalline cohomology groups, including slope numbers, domino numbers, and Hodge-Witt numbers.

AB - We consider derived invariants of varieties in positive characteristic arising from topological Hochschild homology. Using theory developed by Ekedahl and Illusie-Raynaud in their study of the slope spectral sequence, we examine the behavior under derived equivalences of various p-adic quantities related to Hodge-Witt and crystalline cohomology groups, including slope numbers, domino numbers, and Hodge-Witt numbers.

KW - Derived equivalence

KW - Dominoes

KW - Hodge numbers

KW - The de rham-witt complex

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DO - 10.14231/AG-2022-011

M3 - Article

AN - SCOPUS:85129743253

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VL - 9

SP - 364

EP - 399

JO - Algebraic Geometry

JF - Algebraic Geometry

IS - 3

ER -

Derived invariants from topological Hochschild homology

Abstract

Keywords

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