Specialization orders on atom spectra of Grothendieck categories

• Ryo Kanda ^[1]
  1. [1] Nagoya University

     Nagoya University

     Naka-ku, Japón

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 11 (November 2015), 2015, págs. 4907-4952
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2015.03.012
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• Resumen

  • We introduce systematic methods to construct Grothendieck categories from colored quivers and develop a theory of the specialization orders on the atom spectra of Grothendieck categories. We show that any partially ordered set is realized as the atom spectrum of some Grothendieck category, which is an analog of Hochster's result in commutative ring theory. We also show that there exists a Grothendieck category which has empty atom spectrum but has nonempty injective spectrum.