REMARKS ON A CATEGORICAL DEFINITION OF DEGENERATION IN TRIANGULATED CATEGORIES

Alexander Zimmermann (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

This work reports on joint research with Manuel Saorin. For an algebra A over an algebraically closed field k the set of A-module structures on k d forms an affine algebraic variety. The general linear group Gl d (k) acts on this variety and isomorphism classes correspond to orbits under this action. A module M degenerates to a module N if N belongs to the Zariski closure of the orbit of M. Yoshino gave a scheme-theoretic characterisation, and Saorin and Zimmermann generalise this concept to general triangulated categories. We show that this concept has an interpretation in terms of distinguished triangles, analogous to the Riedtmann-Zwara characterisation for modules. In this manuscript we report on these results and study the behaviour of this degeneration concept under functors between triangulated categories.

Mots clés: module varieties; triangulated categories; degeneration

Domaines: Théorie des représentations [math.RT]; Anneaux et algèbres [math.RA]

Alexander Zimmermann. REMARKS ON A CATEGORICAL DEFINITION OF DEGENERATION IN TRIANGULATED CATEGORIES. 47th Symposion on Ring Theory and Representation Theory, Sep 2014, Osaka, Japan. ⟨hal-01160819⟩