Semi-continuity for derived categories
10
TL;DR: In this article, it was shown that the number of parameters defining a complex of projective modules over an algebra is upper semi-continuous in families of algebras.
read more
Abstract: We prove that the number of parameters defining a complex of projective modules over an algebra is upper semi-continuous in families of algebras. The proof follows the pattern of the paper by Drozd and Greuel and rests upon universal families with projective bases. Supposing that every algebra is either derived tame or derived wild, we get that a degeneration of a derived wild algebra is also derived wild. We also discuss an apparent counter-example to the last assertion by Th. Brustle.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
•Posted Content
Tame-wild dichotomy for derived categories
Viktor Bekkert,Yuriy Drozd +1 more
TL;DR: In this article, it was shown that every finite dimensional algebra over an al-gebraically closed field is either derived tame or derived wild, based on the technique of boxes and reduction algorithm.
•Posted Content
Derived tame and derived wild algebras
TL;DR: In this paper, it was shown that every finite dimensional algebra over an algebraically closed field is either derived tame or derived wild, and that any deformation of a derived tame algebra is derived tame.
14
•Posted Content
Derived categories for algebras with radical square zero
Viktor Bekkert,Yuriy Drozd +1 more
TL;DR: In this paper, the derived representation types of algebras with radical square zero were determined and a description of the indecomposable objects in their bounded derived categories was given.
Derived tame local and two-point algebras
TL;DR: In this paper, the derived representation type of complete finitely generated local and two-point algebras over an algebraically closed field is determined. But the problem of determining derived representation types of finite-dimensional local and 2-point algebra is still open.
10
Derived categories of modules and coherent sheaves
Yuriy Drozd
- 01 Apr 2006
TL;DR: In this paper, a survey of recent results on the structure of derived categories obtained by the author in collaboration with Viktor Bekkert and Igor Burban is presented, as well as explicit calculations for derived categories of modules over nodal rings and of coherent sheaves over projective configurations of types A and A.
4
References
Finitistic dimension and a homological generalization of semi-primary rings
TL;DR: In this article, Kaplansky showed that a commutative ring R is left T-nilpotent if, given any sequence {at} of elements in N, there exists an re such that ai • • • an = 0.
•Book
Singularities, Representation of Algebras, and Vector Bundles
Gert-Martin Greuel
- 01 Nov 1987
125