The derived category of complex periodic K-theory localized at an odd prime

Irakli Patchkoria

doi:10.1016/j.aim.2017.01.023

The derived category of complex periodic K-theory localized at an odd prime

Irakli Patchkoria^*

^*Corresponding author for this work

Mathematical Science

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

5 Citations (Scopus)

Abstract

We prove that for an odd prime p, the derived category D(KU_(p))
of the p-local complex periodic K-theory spectrum KU_(p) is triangulated equivalent to the derived category of its homotopy ring pi_*KU_(p). This implies that if p is an odd prime, the triangulated category D(KU_(p)) is algebraic.

Original language	English
Pages (from-to)	392-435
Number of pages	43
Journal	Advances in Mathematics
Volume	309
Early online date	16 Feb 2017
DOIs	https://doi.org/10.1016/j.aim.2017.01.023
Publication status	Published - 17 Mar 2017

Keywords

Derivator
Model category
K-theory
Module spectrum
Stable model category
Triangulated category

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https://www.sciencedirect.com/science/article/pii/S0001870816303589Licence: GNU LGPL

Irakli Patchkoria
- School of Natural & Computing Sciences, Mathematical Science - Lecturer
Person: Academic

Cite this

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title = "The derived category of complex periodic K-theory localized at an odd prime",

abstract = "We prove that for an odd prime p, the derived category D(KU_(p))of the p-local complex periodic K-theory spectrum KU_(p) is triangulated equivalent to the derived category of its homotopy ring pi_*KU_(p). This implies that if p is an odd prime, the triangulated category D(KU_(p)) is algebraic.",

keywords = "Derivator, Model category, K-theory, Module spectrum, Stable model category, Triangulated category",

author = "Irakli Patchkoria",

note = "First of all I would like to thank Tyler Lawson and Stefan Schwede for their interest in the subject and for encouraging me to think about this problem. Special thanks go to Dustin Clausen for answering my questions in Galois theory and to Moritz Groth for tutorials on derivators. I would also like to thank Rasmus Bentmann, Jens Franke, John Greenlees, Snigdhayan Mahanta, George Nadareishvili and Constanze Roitzheim for useful conversations. Finally, I thank the referee for helpful comments. This research was supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92) and the Shota Rustaveli National Science Foundation grant DI/27/5-103/12.",

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doi = "10.1016/j.aim.2017.01.023",

language = "English",

volume = "309",

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journal = "Advances in Mathematics",

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T1 - The derived category of complex periodic K-theory localized at an odd prime

AU - Patchkoria, Irakli

N1 - First of all I would like to thank Tyler Lawson and Stefan Schwede for their interest in the subject and for encouraging me to think about this problem. Special thanks go to Dustin Clausen for answering my questions in Galois theory and to Moritz Groth for tutorials on derivators. I would also like to thank Rasmus Bentmann, Jens Franke, John Greenlees, Snigdhayan Mahanta, George Nadareishvili and Constanze Roitzheim for useful conversations. Finally, I thank the referee for helpful comments. This research was supported by the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92) and the Shota Rustaveli National Science Foundation grant DI/27/5-103/12.

PY - 2017/3/17

Y1 - 2017/3/17

N2 - We prove that for an odd prime p, the derived category D(KU_(p))of the p-local complex periodic K-theory spectrum KU_(p) is triangulated equivalent to the derived category of its homotopy ring pi_*KU_(p). This implies that if p is an odd prime, the triangulated category D(KU_(p)) is algebraic.

AB - We prove that for an odd prime p, the derived category D(KU_(p))of the p-local complex periodic K-theory spectrum KU_(p) is triangulated equivalent to the derived category of its homotopy ring pi_*KU_(p). This implies that if p is an odd prime, the triangulated category D(KU_(p)) is algebraic.

KW - Derivator

KW - Model category

KW - K-theory

KW - Module spectrum

KW - Stable model category

KW - Triangulated category

U2 - 10.1016/j.aim.2017.01.023

DO - 10.1016/j.aim.2017.01.023

M3 - Article

VL - 309

SP - 392

EP - 435

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -

The derived category of complex periodic K-theory localized at an odd prime

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Keywords

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Irakli Patchkoria

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