Moduli of unipotent representations I: foundational topics

Ishai Dan-Cohen[1]

  • [1] Leibniz Universität Hannover Institut für Algebra, Zahlentheorie und Diskrete Mathematik Fakultät für Mathematik und Physik Welfengarten 1 30167 Hannover Germany

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 3, page 1123-1187
  • ISSN: 0373-0956

Abstract

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With this work and its sequel, Moduli of unipotent representations II, we initiate a study of the finite dimensional algebraic representations of a unipotent group over a field of characteristic zero from the modular point of view. Let G be such a group. The stack ℳ n ( G ) of all representations of dimension n is badly behaved. In this first installment, we introduce a nondegeneracy condition which cuts out a substack ℳ n nd ( G ) which is better behaved, and, in particular, admits a coarse algebraic space, which we denote by M n nd ( G ) . We also study the problem of glueing a pair of nondegenerate representations along a common subquotient.

How to cite

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Dan-Cohen, Ishai. "Moduli of unipotent representations I: foundational topics." Annales de l’institut Fourier 62.3 (2012): 1123-1187. <http://eudml.org/doc/251141>.

@article{Dan2012,
abstract = {With this work and its sequel, Moduli of unipotent representations II, we initiate a study of the finite dimensional algebraic representations of a unipotent group over a field of characteristic zero from the modular point of view. Let $G$ be such a group. The stack $\mathcal\{M\}_n(G)$ of all representations of dimension $n$ is badly behaved. In this first installment, we introduce a nondegeneracy condition which cuts out a substack $\mathcal\{M\}_n^\mathrm\{nd\}(G)$ which is better behaved, and, in particular, admits a coarse algebraic space, which we denote by $M_n^\mathrm\{nd\}(G)$. We also study the problem of glueing a pair of nondegenerate representations along a common subquotient.},
affiliation = {Leibniz Universität Hannover Institut für Algebra, Zahlentheorie und Diskrete Mathematik Fakultät für Mathematik und Physik Welfengarten 1 30167 Hannover Germany},
author = {Dan-Cohen, Ishai},
journal = {Annales de l’institut Fourier},
keywords = {unipotent representation; unipotent group action; coarse moduli space; moduli space; nilpotent Lie algebra},
language = {eng},
number = {3},
pages = {1123-1187},
publisher = {Association des Annales de l’institut Fourier},
title = {Moduli of unipotent representations I: foundational topics},
url = {http://eudml.org/doc/251141},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Dan-Cohen, Ishai
TI - Moduli of unipotent representations I: foundational topics
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 3
SP - 1123
EP - 1187
AB - With this work and its sequel, Moduli of unipotent representations II, we initiate a study of the finite dimensional algebraic representations of a unipotent group over a field of characteristic zero from the modular point of view. Let $G$ be such a group. The stack $\mathcal{M}_n(G)$ of all representations of dimension $n$ is badly behaved. In this first installment, we introduce a nondegeneracy condition which cuts out a substack $\mathcal{M}_n^\mathrm{nd}(G)$ which is better behaved, and, in particular, admits a coarse algebraic space, which we denote by $M_n^\mathrm{nd}(G)$. We also study the problem of glueing a pair of nondegenerate representations along a common subquotient.
LA - eng
KW - unipotent representation; unipotent group action; coarse moduli space; moduli space; nilpotent Lie algebra
UR - http://eudml.org/doc/251141
ER -

References

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  13. Gérard Laumon, Laurent Moret-Bailly, Champs algébriques, (2000), Springer-Verlag, Berlin MR1771927
  14. David Mumford, John Fogarty, Frances Kirwan, Geometric invariant theory, third enlarged edition, (2002), Springer-Verlag, Berlin Zbl0797.14004MR1304906
  15. Martin Olsson, Compactifying moduli spaces for abelian varieties, (2008), Springer-Verlag, Berlin and New York Zbl1165.14004MR2446415
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