# McKay Correspondence over Non Algebraically Closed Fields

@article{Blume2014McKayCO,
title={McKay Correspondence over Non Algebraically Closed Fields},
author={Mark Blume},
journal={arXiv: Algebraic Geometry},
year={2014},
pages={47-75}
}
• Mark Blume
• Published 23 January 2006
• Mathematics
• arXiv: Algebraic Geometry
The classical McKay correspondence for finite subgroups G of $$\mathrm{SL}(2, \mathbb{C})$$ 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 $$\mathbb{A}_{\mathbb{C}}^{2}/G$$. Over non algebraically closed fields K there may exist representations irreducible over K which split over $$\overline{K}$$. The same is true for irreducible components of…
1 Citations

## References

SHOWING 1-10 OF 33 REFERENCES
La correspondance de McKay
Let M be a quasiprojective algebraic manifold with K_M=0 and G a finite automorphism group of M acting trivially on the canonical class K_M; for example, a subgroup G of SL(n,C) acting on C^n in the
Mukai implies McKay: the McKay correspondence as an equivalence of derived categories
• Mathematics
• 1999
Let G be a finite group of automorphisms of a nonsingular complex threefold M such that the canonical bundle omega_M is locally trivial as a G-sheaf. We prove that the Hilbert scheme Y=GHilb M
Kleinian singularities, derived categories and Hall algebras
• Mathematics
• 1998
We describe the derived category of coherent sheaves on the minimal resolution of the Kleinian singularity associated to a finite subgroup G of SL(2). Then, we give an application to the
Simple Singularities and Simple Algebraic Groups
Regular group actions.- Deformation theory.- The quotient of the adjoint action.- The resolution of the adjoint quotient.- Subregular singularities.- Simple singularities.- Nilpotent elements in
Construction of G‐Hilbert schemes
In this paper we construct G‐Hilbert schemes for finite group schemes G. We find a construction of G‐Hilbert schemes as relative G‐Hilbert schemes over the quotient that does not need the Hilbert
Hilbert schemes of abelian group orbits.
• Mathematics
• 1999
For G a finite abelian subgroup of SL(3, k) we construct a crepant resolution of the quotient variety A/G in a canonical way.
A Course in Arithmetic
Part 1 Algebraic methods: finite fields p-adic fields Hilbert symbol quadratic forms over Qp, and over Q integral quadratic forms with discriminant +-1. Part 2 Analytic methods: the theorem on
Rational singularities, with applications to algebraic surfaces and unique factorization
© Publications mathématiques de l’I.H.É.S., 1969, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://
Hopf π- Algebras
This paper introduces five notions, including π-algebras, π-ideals, Hopf π-algebras, π-modules and Hopf π-modules, verifies the fundamental isomorphism theorem of π-algebras and studies some
Techniques de construction et théorèmes d'existence en géométrie algébrique IV : les schémas de Hilbert
© Association des collaborateurs de Nicolas Bourbaki, 1961, tous droits réservés. L’accès aux archives du séminaire Bourbaki (http://www.bourbaki. ens.fr/) implique l’accord avec les conditions