The Derived Picard Group is a Locally Algebraic Group
Rings and Algebras
2007-05-23 v2 Algebraic Geometry
Representation Theory
Abstract
Let A be a finite dimensional algebra over an algebraically closed field K. The derived Picard group DPic(A) is the group of two-sided tilting complexes over A modulo isomorphism. We prove that DPic(A) is a locally algebraic group, and its identity component is Out^0(A). If B is a derived Morita equivalent algebra then DPic(A) is isomorphic to DPic(B) as locally algebraic groups. Our results extend, and our based on, work of Huisgen-Zimmermann, Saorin and Rouquier.
Keywords
Cite
@article{arxiv.math/0005005,
title = {The Derived Picard Group is a Locally Algebraic Group},
author = {Amnon Yekutieli},
journal= {arXiv preprint arXiv:math/0005005},
year = {2007}
}
Comments
4 pages, AMSLaTeX, to appear in Algebr. Represent. Theory