Riemann–Roch like theorem for triangulated categories
نویسندگان
چکیده
منابع مشابه
Universal coe cient theorem in triangulated categories
We consider a homology theory h : T ! A on a triangulated category T with values in a graded abelian category A . If the functor h re ects isomorphisms, is full and is such that for any object x in A there is an object X in T with an isomorphism between h(X) and x, we prove that A is a hereditary abelian category, all idempotents in T split and the kernel of h is a square zero ideal which as a ...
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Contents 1. Introduction 1 2. Categories of fractions and localization functors 3 3. Calculus of fractions 9 4. Localization for triangulated categories 13 5. Localization via Brown representatbility 23 6. Well generated triangulated categories 31 7. Localization for well generated categories 38 8. Epilogue: Beyond well-generatedness 46 Appendix A. The abelianization of a triangulated category ...
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We study cocoverings of triangulated categories, in the sense of Rouquier, and prove that for any regular cardinal α the condition of α-compactness, in the sense of Neeman, is local with respect to such cocoverings. This was established for ordinary compactness by Rouquier. Our result yields a new technique for proving that a given triangulated category is well-generated. As an application we d...
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Contents 1. Introduction 1 2. Categories of fractions and localization functors 3 3. Calculus of fractions 9 4. Localization for triangulated categories 14 5. Localization via Brown representability 24 6. Well generated triangulated categories 31 7. Localization for well generated categories 39 8. Epilogue: Beyond well generatedness 47 Appendix A. The abelianization of a triangulated category 4...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2004
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2004.03.008