Comptes Rendus
no. 2
Geometry/Topology
Projective representations of fundamental groups of quasiprojective varieties: a realization and a lifting result

Presented by: Étienne Ghys

Gaël Cousin1
1 Università di Pisa, Dipartimento di Matematica, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
Comptes Rendus. Mathématique, Volume 353 (2015) no. 2, pp. 155-159.

We discuss two results about projective representations of fundamental groups of quasiprojective varieties. The first is a realization result that, under a nonresonance assumption, allows us to realize such representations as monodromy representations of flat projective logarithmic connections. The second is a lifting result: any representation as above, after restriction to a Zariski open set and finite pull-back, can be lifted to a linear representation.

Nous discutons deux résultats sur les représentations projectives des groupes fondamentaux de variétés quasi-projectives. Le premier est un résultat de réalisation qui, sous une hypothèse de non-résonance, permet de réaliser ces représentations comme représentations de monodromie de connexions projectives plates logarithmiques. Le second est un résultat de relèvement : après restriction à un ouvert de Zariski et un revêtement fini, toute représentation du type considéré se relève en une représentation linéaire.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2014.11.011

Gaël Cousin 1

1 Università di Pisa, Dipartimento di Matematica, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy 
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Gaël Cousin. Projective representations of fundamental groups of quasiprojective varieties: a realization and a lifting result. Comptes Rendus. Mathématique, Volume 353 (2015) no. 2, pp. 155-159. doi : 10.1016/j.crma.2014.11.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.11.011/

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