348 research outputs found
Lectures on derived and triangulated categories
These notes are meant to provide a rapid introduction to triangulated
categories. We start with the definition of an additive category and end with a
glimps of tilting theory. Some exercises are included.Comment: Lecture notes. To appear in the proceedings volume of the
"International Workshop on Noncommutative Geometry", IPM, Tehran 200
Explicit HRS-Tilting
For an abelian category equipped with a torsion pair, we give an explicit
description for the abelian category introduced by Happel-Reiten-Smalo, and
also for the category of chain complexes and the derived category
of . We also describe the DG structure on . As a consequence,
we find new proofs of certain results of Happel-Reiten-Smalo. The main
ingredient is the category of {\em decorated} complexes.Comment: 31 pages, introduction expanded, minor errors correcte
Uniformization of Deligne-Mumford curves
We compute the fundamental groups of non-singular analytic Deligne-Mumford
curves, classify the simply connected ones, and classify analytic
Deligne-Mumford curves by their uniformization type. As a result, we find an
explicit presentation of an arbitrary Deligne-Mumford curve as a quotient
stack. Along the way, we compute the automorphism 2-groups of weighted
projective stacks . We also discuss connections
with the theory of F-groups, 2-groups, and Bass-Serre theory of graphs of
groups.Comment: 39 pages, 2 figure
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