HIGHER SEMIADDITIVE GROTHENDIECK-WITT THEORY AND THE K(1)-LOCAL SPHERE

Shachar Carmeli; Allen Yuan

doi:10.1090/cams/17

HIGHER SEMIADDITIVE GROTHENDIECK-WITT THEORY AND THE K(1)-LOCAL SPHERE

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

Abstract

We develop a higher semiadditive version of Grothendieck-Witt theory. We then apply the theory in the case of a finite field to study the higher semiadditive structure of the K(1)-local sphere SK(1) at the prime 2, in particular realizing the non-2-adic rational element 1 + ε π0SK(1) as a “semiadditive cardinality.” As a further application, we compute and clarify certain power operations in π0SK(1).

Original language	English
Pages (from-to)	65-111
Number of pages	47
Journal	Communications of the American Mathematical Society
Volume	3
DOIs	https://doi.org/10.1090/cams/17
State	Published - 2023
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)
Applied Mathematics

Access to Document

10.1090/cams/17

Cite this

@article{5a72ce0da37542b7b82cbd5a2b60088f,

title = "HIGHER SEMIADDITIVE GROTHENDIECK-WITT THEORY AND THE K(1)-LOCAL SPHERE",

abstract = "We develop a higher semiadditive version of Grothendieck-Witt theory. We then apply the theory in the case of a finite field to study the higher semiadditive structure of the K(1)-local sphere SK(1) at the prime 2, in particular realizing the non-2-adic rational element 1 + ε π0SK(1) as a “semiadditive cardinality.” As a further application, we compute and clarify certain power operations in π0SK(1).",

author = "Shachar Carmeli and Allen Yuan",

note = "Publisher Copyright: {\textcopyright} 2023 by the author(s) under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License (CC BY NC ND 4.0).",

year = "2023",

doi = "10.1090/cams/17",

language = "الإنجليزيّة",

volume = "3",

pages = "65--111",

}

TY - JOUR

T1 - HIGHER SEMIADDITIVE GROTHENDIECK-WITT THEORY AND THE K(1)-LOCAL SPHERE

AU - Carmeli, Shachar

AU - Yuan, Allen

PY - 2023

Y1 - 2023

N2 - We develop a higher semiadditive version of Grothendieck-Witt theory. We then apply the theory in the case of a finite field to study the higher semiadditive structure of the K(1)-local sphere SK(1) at the prime 2, in particular realizing the non-2-adic rational element 1 + ε π0SK(1) as a “semiadditive cardinality.” As a further application, we compute and clarify certain power operations in π0SK(1).

AB - We develop a higher semiadditive version of Grothendieck-Witt theory. We then apply the theory in the case of a finite field to study the higher semiadditive structure of the K(1)-local sphere SK(1) at the prime 2, in particular realizing the non-2-adic rational element 1 + ε π0SK(1) as a “semiadditive cardinality.” As a further application, we compute and clarify certain power operations in π0SK(1).

UR - http://www.scopus.com/inward/record.url?scp=105003050936&partnerID=8YFLogxK

U2 - 10.1090/cams/17

DO - 10.1090/cams/17

M3 - مقالة

VL - 3

SP - 65

EP - 111

JO - Communications of the American Mathematical Society

JF - Communications of the American Mathematical Society

ER -

HIGHER SEMIADDITIVE GROTHENDIECK-WITT THEORY AND THE K(1)-LOCAL SPHERE

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this