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McKay correspondence over non algebraically closed fields

Authors
  • Blume, Mark
Type
Published Article
Publication Date
Jul 01, 2013
Submission Date
Jan 23, 2006
Identifiers
arXiv ID: math/0601550
Source
arXiv
License
Yellow
External links

Abstract

The classical McKay correspondence for finite subgroups $G$ of $\SL(2,\C)$ gives a bijection between isomorphism classes of nontrivial irreducible representations of $G$ and irreducible components of the exceptional divisor in the minimal resolution of the quotient singularity $\A^2_\C/G$. Over non algebraically closed fields $K$ there may exist representations irreducible over $K$ which split over $\bar{K}$. The same is true for irreducible components of the exceptional divisor. In this paper we show that these two phenomena are related and that there is a bijection between nontrivial irreducible representations and irreducible components of the exceptional divisor over non algebraically closed fields $K$ of characteristic 0 as well.

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