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K-theory and Noncommutative Geometry.pdf

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412 G. Garkusha and M. PrestReferences[1] M. Artin, J. J. Zhang, Noncommutative projective schemes, Adv. Math. 109(2) (1994),228–287.[2] M. F. Atiyah, I. G. Macdonald, Introduction to commutative algebra, Addison-WesleyPublishing Co., Reading, Mass, 1969.[3] P. Balmer, Presheaves of triangulated categories and reconstruction of schemes, Math. Ann.324(3) (2002), 557–580.[4] P. Balmer, The spectrum of prime ideals in tensor triangulated categories, J. Reine Angew.Math. 588 (2005), 149–168.[5] A. B. Buan, H. Krause, Ø. Solberg, Support varieties – an ideal approach, Homology,Homotopy Appl. 9 (2007), 45–74.[6] P. Gabriel, Des catégories abeliénnes, Bull. Soc. Math. France 90 (1962), 323–448.[7] G. Garkusha, Grothendieck categories, Algebra i Analiz 13(2) (2001), 1–68; English transl.St. Petersburg Math. J. 13 (2002), 149–200.[8] G. Garkusha, M. Prest, Classifying Serre subcategories of finitely presented modules, Proc.Amer. Math. Soc. 136 (2008), 761–770.[9] G. Garkusha, M. Prest, Reconstructing projective schemes from Serre subcategories, J. Algebra319 (2008), 1132–1153.[10] M. Hochster, Prime ideal structure in commutative rings, Trans. Amer. Math. Soc. 142(1969), 43–60.[11] M. Hovey, Classifying subcategories of modules, Trans. Amer. Math. Soc. 353 (2001),3181—3191.[12] P. T. Johnstone, Stone Spaces, Cambridge Stud. in Adv. Math. 3, Cambridge UniversityPress, Cambridge 1982.[13] Ch. Kassel, Quantum groups, Grad. Texts in Math. 155, Springer-Verlag, New York 1995.[14] M. Prest, The Zariski spectrum of the category of finitely presented modules, preprintavailable at maths.man.ac.uk/mprest.[15] A. L. Rosenberg, The spectrum of abelian categories and reconstruction of schemes, inRings, Hopf algebras, and Brauer groups, Lect. Notes PureAppl. Math. 197, Marcel Dekker,New York 1998, 257–274.[16] J. T. Stafford, Noncommutative projective geometry, in Proceedings of the InternationalCongress of Mathematicians (Beijing, 2002), Vol. II, Higher Ed. Press, Beijing 2002,93–103.[17] B. Stenström, Rings of quotients, Grundlehren Math. Wiss. 217, Springer-Verlag, Berlin,Heidelberg, New York 1975.[18] R. W. Thomason, The classification of triangulated subcategories, Compos. Math. 105(1997), 1–27.[19] A. B. Verevkin, On a noncommutative analogue of the category of coherent sheaves on aprojective scheme, in Algebra and analysis (Tomsk, 1989), Amer. Math. Soc. Transl. (2)151, Amer. Math. Soc., Providence, RI, 1992.[20] M. Ziegler, Model theory of modules, Ann. Pure Appl. Logic 26 (1984), 149–213.

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