Noncommutative Counterparts of the Springer Resolution
Abstract
Springer resolution of the set of nilpotent elements in a semisimple Lie algebra plays a central role in geometric representation theory. A new structure on this variety has arisen in several representation theoretic constructions, such as the (local) geometric Langlands duality and modular representation theory. It is also related to some algebro-geometric problems, such as the derived equivalence conjecture and description of T. Bridgeland's space of stability conditions. The structure can be described as a noncommutative counterpart of the resolution, or as a -structure on the derived category of the resolution. The intriguing fact that the same -structure appears in these seemingly disparate subjects has strong technical consequences for modular representation theory.
Keywords
Cite
@article{arxiv.math/0604445,
title = {Noncommutative Counterparts of the Springer Resolution},
author = {Roman Bezrukavnikov},
journal= {arXiv preprint arXiv:math/0604445},
year = {2007}
}
Comments
ICM talk; 23 pages