Mathematische Zeitschrift

, Volume 254, Issue 1, pp 133–171

Hereditary noetherian categories of positive Euler characteristic

Article

DOI: 10.1007/s00209-006-0938-6

Cite this article as:
Lenzing, H. & Reiten, I. Math. Z. (2006) 254: 133. doi:10.1007/s00209-006-0938-6

Abstract

We develop the fundamentals of hereditary noetherian categories with Serre duality over an arbitrary field k, where the category of coherent sheaves over a smooth projective curve over k serves as the prime example and others are coming from the representation theory of finite dimensional algebras. The proper way to view such a category is to think of coherent sheaves on a possibly non-commutative smooth projective curve. We define for each such category notions like function field and Euler characteristic, determine its Auslander-Reiten components and study stable and semistable bundles for an appropriate notion of degree. We provide a complete classification of hereditary noetherian categories for the case of positive Euler characteristic by relating these to finite dimensional representations of (locally bounded) hereditary k-algebras whose underlying valued quiver admits a positive additive function.

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Institut für MathematikUniversität PaderbornPaderbornGermany
  2. 2.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway

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