Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-31T23:20:01.541Z Has data issue: false hasContentIssue false
  • English
  • Français

The affine part of the Picard scheme

Part of: Abelian varieties and schemes

Published online by Cambridge University Press:  01 March 2009

Thomas Geisser
Thomas Geisser*
Affiliation:
Department of Mathematics, University of Southern California, 3620 S Vermont Av. KAP 108, Los Angeles, CA 90089-2532, USA (email: [email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We describe the maximal torus and maximal unipotent subgroup of the Picard variety of a proper scheme over a perfect field.

Keywords

Picard schemetorusunipotent subgroupsemi-normalizationétale cohomology

MSC classification

Secondary: 14K30: Picard schemes, higher Jacobians
Type
Research Article
Information
Compositio Mathematica , Volume 145 , Issue 2 , March 2009 , pp. 415 - 422
Copyright
Copyright © Foundation Compositio Mathematica 2009

References

[1]Bosch, S., Lütkebohmert, W. and Raynaud, M., Neron models, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 21 (Springer, Berlin, 1990).Google Scholar
[2]Chevalley, C., Une démonstration d’un théorème sur les groupes algébriques, J. Math. Pures Appl. (9) 39 (1960), 307–317.Google Scholar
[3]Geisser, T., Arithmetic cohomology over finite fields and special values of ζ-functions, Duke Math. J. 133 (2006), 27–57.CrossRefGoogle Scholar
[4]Geisser, T., Duality via cycle complexes, Ann. of Math (2), to appear, arXiv:math.AG/0608456.Google Scholar
[5]Grothendieck, A., Technique de descente et théoremes d’existence en géometrie algébrique. VI. Les schémas de Picard: propriétés générales, in Seminaire Bourbaki, 1961/62, Exposé no. 236 (Société Mathématique de France, Paris, 1962).Google Scholar
[6]Milne, J.S., Étale cohomology, Princeton Mathematical Series, vol. 33 (Princeton University Press, Princeton, NJ, 1980).Google Scholar
[7]Murre, J.P., On contravariant functors from the category of pre-schemes over a field into the category of abelian groups (with an application to the Picard functor), Publ. Math. Inst. Hautes Études Sci. 23 (1964), 5–43.CrossRefGoogle Scholar
[8]Oort, F., Sur le schéma de Picard, Bull. Soc. Math. France 90 (1962), 1–14.Google Scholar
[9]Oort, F., Commutative group schemes, Lecture Notes in Mathematics, vol. 15 (Springer, Berlin, 1966).Google Scholar
[10]Raynaud, M., Spécialisation du foncteur de Picard, Publ. Math. Inst. Hautes Études Sci. 38 (1970), 27–76.CrossRefGoogle Scholar
[11]Roberts, L. and Singh, B., Subintegrality, invertible modules and the Picard group, Compositio Math. 85 (1993), 249–279.Google Scholar
[12]Raynaud, M., Groups algébriques unipotents. Extensions entre groupes unipotents et groupes de type multiplicative, in Séminarie de Géometrie Algébrique du Bois Marie 1963/64 (SGA3), Lecture Notes in Mathematics, vol. 152 (Springer, Berlin, 1970).Google Scholar
[13]Traverso, C., Seminormality and Picard group, Ann. Sc. Norm. Super. Pisacl. Sci. (3) 24 (1970), 585–595.Google Scholar
[14]Weibel, C., Pic is a contracted functor, Invent. Math. 103 (1991), 351–377.CrossRefGoogle Scholar