Triangulated CategoriesThorsten Holm, Peter Jørgensen, Raphaël Rouquier Cambridge University Press, 24 giu 2010 Over the last few decades triangulated categories have become increasingly important, to the extent that they can now be viewed as a unifying theory underlying major parts of modern mathematics. This 2010 collection of survey articles, written by leading experts, covers fundamental aspects of triangulated categories, as well as applications in algebraic geometry, representation theory, commutative algebra, microlocal analysis and algebraic topology. These self-contained articles are a useful introduction for graduate students entering the field and a valuable reference for experts. |
Sommario
Cohomology over complete intersections via exterior algebras | 52 |
Cluster algebras quiver representations and triangulated | 76 |
Localization theory for triangulated categories | 161 |
Homological algebra in bivariant Ktheory and other | 236 |
Derived categories and Grothendieck duality | 290 |
Derived categories and algebraic geometry | 351 |
Triangulated categories for the analysts | 371 |
Algebraic versus topological triangulated categories | 389 |
Derived categories of coherent sheaves on algebraic varieties | 408 |
Rigid dualizing complexes via differential graded algebras | 452 |
Altre edizioni - Visualizza tutto
Triangulated Categories Thorsten Holm,Peter Jørgensen,Raphaël Rouquier Anteprima non disponibile - 2010 |
Parole e frasi comuni
A-module abelian category abelian groups additive category affine arrows bijection canonical chain complex cluster algebra cluster category cluster variables cluster-tilting coefficients coherent sheaves cohomology colimits commutative compact object construction D(Qcoh/X Db(Coh/X define Definition denote derived category derived functors DG algebra diagram dimension direct sums distinguished triangle dualizing complex equivalence exact functor exact triangle example exists field finite first full subcategory fully faithful functor F Grothendieck hence homomorphism homotopy category I-exact I-projective ideal indecomposable induces injective integer invertible kernel left adjoint Lemma Let F mapping cone Math modules morphism morphism f mutation Ñ Ñ Ñ noetherian phism preserves small coproducts Proof Proposition quasi-isomorphism quasicompact quotient Remark representations resolution right adjoint ring satisfies Serre sheaf short exact sequence space stability conditions structure Suppose Theorem theory thick subcategory topology triangulated category triangulated subcategory unique vector vertex zero