The Symmetric Signature
Ph.D. Thesis, University of Osnabrück, 2016
(Sprache: Englisch)
This is a dissertation in commutative algebra. The author introduces a new numerical invariant for local rings called symmetric signature. Given a local ring, the symmetric signature is defined by looking at the maximal free splitting of reflexive symmetric...
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This is a dissertation in commutative algebra. The author introduces a new numerical invariant for local rings called symmetric signature. Given a local ring, the symmetric signature is defined by looking at the maximal free splitting of reflexive symmetric powers of the top-dimensional syzygy module of the residue field. The main motivation for this work is given by the F-signature, an important numerical invariant for local rings of positive characteristic which has been largely studied in the last decade. The dissertation contains a computation of the symmetric signature for two-dimensional ADE singularities and for cones over elliptic curves. In both cases, the values obtained coincide with the F-signature of such rings in positive characteristic. The thesis presents also a self-contained exposition of the Auslander correspondence, which is one of the main methods employed.
Bibliographische Angaben
- Autor: Alessio Caminata
- 2017, 148 Seiten, Maße: 22 cm, Kartoniert (TB), Englisch
- Verlag: AV Akademikerverlag
- ISBN-10: 3330520663
- ISBN-13: 9783330520660
Sprache:
Englisch
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