The Symmetric Signature - Caminata, Alessio
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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…mehr

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Produktbeschreibung
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.
Autorenporträt
Alessio Caminata received his Ph.D. in Mathematics in 2016 from the University of Osnabrück. After one year as a postdoc at the University of Neuchâtel, he moved to the University of Barcelona with a Marie Sk¿odowska-Curie individual fellowship.His research interests are in commutative algebra, algebraic geometry, and post-quantum cryptography.