ON THE COHOMOLOGY GROUPS OF LOCAL SYSTEMS OVER HILBERT MODULAR VARIETIES VIA HIGGS BUNDLES

Publikationstyp:
Zeitschriftenaufsatz
Metadaten:
Autoren
Autoren-URL
https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=fis-test-1&SrcAuth=WosAPI&KeyUT=WOS:000348969800001&DestLinkType=FullRecord&DestApp=WOS_CPL
eISSN
1080-6377
Externe Identifier
  • Clarivate Analytics Document Solution ID: CA5TD
ISSN
0002-9327
Ausgabe der Veröffentlichung
1
Zeitschrift
AMERICAN JOURNAL OF MATHEMATICS
Paginierung
1 - 35
Datum der Veröffentlichung
2015
Status
Published
Titel
ON THE COHOMOLOGY GROUPS OF LOCAL SYSTEMS OVER HILBERT MODULAR VARIETIES VIA HIGGS BUNDLES
Sub types
  • Article
Ausgabe der Zeitschrift
137

Datenquelle: Web of Science (Lite)

Andere Metadatenquellen:
Abstract
Let $X$ be a Hilbert modular variety and $\mathbb{V}$ a non-trivial local system over $X$ with infinite monodromy. In this paper we study Saito's mixed Hodge structure (MHS) on the cohomology group $H^k(X,\mathbb{V})$ using the method of Higgs bundles. Among other results we prove the Eichler-Shimura isomorphism, give a dimension formula for the Hodge numbers and show that the mixed Hodge structure is split over $\mathbb{R}$. These results are analogous to Matsushima-Shimura [Annals of Mathematics 78, 1963] in the cocompact case and complement the results in Freitag [Book: Hilbert modular forms, Springer-Verlag, Berlin, 1990] for constant coefficients.
Autoren
Autoren-URL
http://arxiv.org/abs/1009.2011v3
Schlüsselwörter
  • math.AG
  • math.AG
  • 11F75, 11F41, 14C30
Notes
38 pages, to appear in American Journal of Mathematics
Datum der Veröffentlichung
2010
Datum der Datenerfassung
2010
Datum, an dem der Datensatz öffentlich gemacht wurde
2010
Titel
On the cohomology groups of local systems over Hilbert modular varieties via Higgs bundles

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1009.2011v3.pdf

Datenquelle: arXiv

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