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Payam Bahiraei - One of the best experts on this subject based on the ideXlab platform.

  • cotorsion pairs and adjoint functors in the Homotopy Category of n complexes
    Journal of Algebra and Its Applications, 2019
    Co-Authors: Payam Bahiraei
    Abstract:

    In this paper, we first construct some complete cotorsion pairs on the Category ℂN(𝒢) of unbounded N-complexes of Grothendieck Category 𝒢, from two given cotorsion pairs in 𝒢. Next, as an applicati...

  • cotorsion pairs and adjoint functors in the Homotopy Category of n complexes
    arXiv: Representation Theory, 2019
    Co-Authors: Payam Bahiraei
    Abstract:

    In this paper, we first construct some complete cotorson pairs on the Category $\mathbb{C}_N(\mathcal{G})$ of unbounded $N$-complexes of Grothendieck Category $\mathcal{G}$, from two given cotorsion pairs in $\mathcal{G}$. Next as an application, we focus on particular Homotopy categories and the existence of adjoint functors between them. These are an $N$-complex version of the results were shown by Neeman in the Category of ordinary complexes.

  • Homotopy Category of n complexes of projective modules
    Journal of Pure and Applied Algebra, 2016
    Co-Authors: Payam Bahiraei, Rasool Hafezi, Amin Nematbakhsh
    Abstract:

    In this paper, we show that the Homotopy Category of N-complexes of pro- jective R-modules is triangle equivalent to the Homotopy Category of projective TN´1pRq- module where TN´1pRq is the ring of triangular matrix with entries in R. We also define the notions of N-singularity Category and N-totally acyclic complexes. We show that the Category of N-totally acyclic complexes of finitely generated projective R-modules em- beds in the N-singularity Category, i.e. a result analogous to the case of ordinary chain complexes.

  • Homotopy Category of n complexes of projective modules
    arXiv: Representation Theory, 2015
    Co-Authors: Payam Bahiraei, Rasool Hafezi, Amin Nematbakhsh
    Abstract:

    In this paper, we show that the Homotopy Category of N-complexes of projective R-modules is triangle equivalent to the Homotopy Category of projective T_{N-1}(R)- modules where T_{N-1}(R) is the ring of triangular matrices of order N-1 with entries in R. We also define the notions of N-singularity Category and N-totally acyclic complexes. We show that the Category of N-totally acyclic complexes of finitely generated projective R-modules embeds in the N-singularity Category, which is a result analogous to the case of ordinary chain complexes.

Omar Jaramillo - One of the best experts on this subject based on the ideXlab platform.

Erik Backelin - One of the best experts on this subject based on the ideXlab platform.

Nathaniel Stapleton - One of the best experts on this subject based on the ideXlab platform.

  • the balmer spectrum of the equivariant Homotopy Category of a finite abelian group
    Inventiones Mathematicae, 2019
    Co-Authors: Tobias Barthel, Niko Naumann, Markus Hausmann, Thomas Nikolaus, Justin Noel, Nathaniel Stapleton
    Abstract:

    For a finite abelian group A, we determine the Balmer spectrum of \({\mathrm {Sp}}_A^{\omega }\), the compact objects in genuine A-spectra. This generalizes the case \(A={\mathbb {Z}}/p{\mathbb {Z}}\) due to Balmer and Sanders (Invent Math 208(1):283–326, 2017), by establishing (a corrected version of) their \(\hbox {log}_p\)-conjecture for abelian groups. We also work out the consequences for the chromatic type of fixed-points and establish a generalization of Kuhn’s blue-shift theorem for Tate-constructions (Kuhn in Invent Math 157(2):345–370, 2004).

  • the balmer spectrum of the equivariant Homotopy Category of a finite abelian group
    arXiv: Algebraic Topology, 2017
    Co-Authors: Tobias Barthel, Niko Naumann, Markus Hausmann, Thomas Nikolaus, Justin Noel, Nathaniel Stapleton
    Abstract:

    For a finite abelian group $A$, we determine the Balmer spectrum of $\mathrm{Sp}_A^{\omega}$, the compact objects in genuine $A$-spectra. This generalizes the case $A=\mathbb{Z}/p\mathbb{Z}$ due to Balmer and Sanders \cite{Balmer-Sanders}, by establishing (a corrected version of) their log$_p$-conjecture for abelian groups. We work out the consequences for the chromatic type of fixed-points. We also establish a generalization of Kuhn's blue-shift theorem for Tate-constructions \cite{kuhn}.

Amin Nematbakhsh - One of the best experts on this subject based on the ideXlab platform.

  • Homotopy Category of n complexes of projective modules
    Journal of Pure and Applied Algebra, 2016
    Co-Authors: Payam Bahiraei, Rasool Hafezi, Amin Nematbakhsh
    Abstract:

    In this paper, we show that the Homotopy Category of N-complexes of pro- jective R-modules is triangle equivalent to the Homotopy Category of projective TN´1pRq- module where TN´1pRq is the ring of triangular matrix with entries in R. We also define the notions of N-singularity Category and N-totally acyclic complexes. We show that the Category of N-totally acyclic complexes of finitely generated projective R-modules em- beds in the N-singularity Category, i.e. a result analogous to the case of ordinary chain complexes.

  • Homotopy Category of n complexes of projective modules
    arXiv: Representation Theory, 2015
    Co-Authors: Payam Bahiraei, Rasool Hafezi, Amin Nematbakhsh
    Abstract:

    In this paper, we show that the Homotopy Category of N-complexes of projective R-modules is triangle equivalent to the Homotopy Category of projective T_{N-1}(R)- modules where T_{N-1}(R) is the ring of triangular matrices of order N-1 with entries in R. We also define the notions of N-singularity Category and N-totally acyclic complexes. We show that the Category of N-totally acyclic complexes of finitely generated projective R-modules embeds in the N-singularity Category, which is a result analogous to the case of ordinary chain complexes.