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Displaying similar documents to “Tilting sheaves in representation theory of algebras.”

General sheaves over weighted projective lines

William Crawley-Boevey (2008)

Colloquium Mathematicae

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We develop a theory of general sheaves over weighted projective lines. We define and study a canonical decomposition, analogous to Kac's canonical decomposition for representations of quivers, study subsheaves of a general sheaf, general ranks of morphisms, and prove analogues of Schofield's results on general representations of quivers. Using these, we give a recursive algorithm for computing properties of general sheaves. Many of our results are proved in a more abstract setting, involving...

Selfinjective algebras of wild canonical type

Helmut Lenzing, Andrzej Skowroński (2003)

Colloquium Mathematicae

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We develop the representation theory of selfinjective algebras which admit Galois coverings by the repetitive algebras of algebras whose derived category of bounded complexes of finite-dimensional modules is equivalent to the derived category of coherent sheaves on a weighted projective line with virtual genus greater than one.

Left-right projective bimodules and stable equivalences of Morita type

Zygmunt Pogorzały (2001)

Colloquium Mathematicae

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We study a connection between left-right projective bimodules and stable equivalences of Morita type for finite-dimensional associative algebras over a field. Some properties of the category of all finite-dimensional left-right projective bimodules for self-injective algebras are also given.

The stack of microlocal perverse sheaves

Ingo Waschkies (2004)

Bulletin de la Société Mathématique de France

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In this paper we construct the abelian stack of microlocal perverse sheaves on the projective cotangent bundle of a complex manifold. Following ideas of Andronikof we first consider microlocal perverse sheaves at a point using classical tools from microlocal sheaf theory. Then we will use Kashiwara-Schapira’s theory of analytic ind-sheaves to globalize our construction. This presentation allows us to formulate explicitly a global microlocal Riemann-Hilbert correspondence.