Moduli spaces for principal bundles in large characteristic

This paper addresses the problem of constructing and compactifying moduli spaces of stable principal G -bundles over smooth projective schemes for an arbitrary reductive group G in both zero and nonzero characteristic. This involves refining the methods of the third author [Transform. Groups 9 (2004...

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Detalles Bibliográficos
Autores: Gómez Tomás, L., Langer, Adrián, Schmitt, Alexander H.W., Sols Lucía, Ignacio
Tipo de recurso: artículo
Fecha de publicación:2008
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/50555
Acceso en línea:https://hdl.handle.net/20.500.14352/50555
Access Level:acceso abierto
Palabra clave:512
Principal bundle
Moduli space
Positive characteristic
Semistable reduction
Semistability
Álgebra
1201 Álgebra
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spelling Moduli spaces for principal bundles in large characteristicGómez Tomás, L.Langer, AdriánSchmitt, Alexander H.W.Sols Lucía, Ignacio512Principal bundleModuli spacePositive characteristicSemistable reductionSemistabilityÁlgebra1201 ÁlgebraThis paper addresses the problem of constructing and compactifying moduli spaces of stable principal G -bundles over smooth projective schemes for an arbitrary reductive group G in both zero and nonzero characteristic. This involves refining the methods of the third author [Transform. Groups 9 (2004), no. 2, 167–209; Int. Math. Res. Not. 2004, no. 62, 3327–3366;] and creating a unified formulation of the results of these papers and a paper of the first and fourth authors [Ann. of Math. (2) 161 (2005), no. 2, 1037–1092;]. The paper also complements a previous article by all four authors [Adv. Math. 219 (2008), no. 4, 1177–1245]. Particular features of the paper are the inclusion of non-semisimple groups and non-faithful representations of G , a new approach to obtaining the semistable reduction theorem in characteristic zero and in large positive characteristic and a construction of the moduli space of decorated sheaves over projective varieties in arbitrary characteristic. The first main theorem states that, in characteristic zero and in large positive characteristic, coarse moduli spaces for (semi)stable singular principal G -bundles can be defined using faithful representations (under some conditions) and exist as projective schemes. This covers many known cases, for example when G is semisimple, for G=GL(V) , also for G one of the classical groups O r (k) , SO r (k) and Sp r (k) provided the characteristic is not 2 and for groups of adjoint type. In order to use a non-faithful representation ρ , singular principal G -bundles must be replaced by principal ρ -sheaves. The second main theorem states that the corresponding coarse moduli spaces exist as quasi-projective schemes provided the base scheme is a curve or the characteristic is zero. Both types of moduli space can be considered as compactifications of the moduli space of slope-stable rational principal G -bundles.ElsevierBiswas, IndranilKulkarni, Ravi S.Mitra, SudebUniversidad Complutense de Madrid20082008-01-0120082008-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/50555reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/505552026-06-02T12:44:21Z
dc.title.none.fl_str_mv Moduli spaces for principal bundles in large characteristic
title Moduli spaces for principal bundles in large characteristic
spellingShingle Moduli spaces for principal bundles in large characteristic
Gómez Tomás, L.
512
Principal bundle
Moduli space
Positive characteristic
Semistable reduction
Semistability
Álgebra
1201 Álgebra
title_short Moduli spaces for principal bundles in large characteristic
title_full Moduli spaces for principal bundles in large characteristic
title_fullStr Moduli spaces for principal bundles in large characteristic
title_full_unstemmed Moduli spaces for principal bundles in large characteristic
title_sort Moduli spaces for principal bundles in large characteristic
dc.creator.none.fl_str_mv Gómez Tomás, L.
Langer, Adrián
Schmitt, Alexander H.W.
Sols Lucía, Ignacio
author Gómez Tomás, L.
author_facet Gómez Tomás, L.
Langer, Adrián
Schmitt, Alexander H.W.
Sols Lucía, Ignacio
author_role author
author2 Langer, Adrián
Schmitt, Alexander H.W.
Sols Lucía, Ignacio
author2_role author
author
author
dc.contributor.none.fl_str_mv Biswas, Indranil
Kulkarni, Ravi S.
Mitra, Sudeb
Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 512
Principal bundle
Moduli space
Positive characteristic
Semistable reduction
Semistability
Álgebra
1201 Álgebra
topic 512
Principal bundle
Moduli space
Positive characteristic
Semistable reduction
Semistability
Álgebra
1201 Álgebra
description This paper addresses the problem of constructing and compactifying moduli spaces of stable principal G -bundles over smooth projective schemes for an arbitrary reductive group G in both zero and nonzero characteristic. This involves refining the methods of the third author [Transform. Groups 9 (2004), no. 2, 167–209; Int. Math. Res. Not. 2004, no. 62, 3327–3366;] and creating a unified formulation of the results of these papers and a paper of the first and fourth authors [Ann. of Math. (2) 161 (2005), no. 2, 1037–1092;]. The paper also complements a previous article by all four authors [Adv. Math. 219 (2008), no. 4, 1177–1245]. Particular features of the paper are the inclusion of non-semisimple groups and non-faithful representations of G , a new approach to obtaining the semistable reduction theorem in characteristic zero and in large positive characteristic and a construction of the moduli space of decorated sheaves over projective varieties in arbitrary characteristic. The first main theorem states that, in characteristic zero and in large positive characteristic, coarse moduli spaces for (semi)stable singular principal G -bundles can be defined using faithful representations (under some conditions) and exist as projective schemes. This covers many known cases, for example when G is semisimple, for G=GL(V) , also for G one of the classical groups O r (k) , SO r (k) and Sp r (k) provided the characteristic is not 2 and for groups of adjoint type. In order to use a non-faithful representation ρ , singular principal G -bundles must be replaced by principal ρ -sheaves. The second main theorem states that the corresponding coarse moduli spaces exist as quasi-projective schemes provided the base scheme is a curve or the characteristic is zero. Both types of moduli space can be considered as compactifications of the moduli space of slope-stable rational principal G -bundles.
publishDate 2008
dc.date.none.fl_str_mv 2008
2008-01-01
2008
2008-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/50555
url https://hdl.handle.net/20.500.14352/50555
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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