Skip to main content
×
×
Home

On the action of the unitary group on the projective plane over a local field

  • Harm Voskuil (a1)
Abstract

Let G be a unitary group of rank one over a non-archimedean local field K (whose residue field has a characteristic ≠ 2). We consider the action of G on the projective plane. A G(K) equivariant map from the set of points in the projective plane that are semistable for every maximal K split torus in G to the set of convex subsets of the building of G(K) is constructed. This map gives rise to an equivariant map from the set of points that are stable for every maximal K split torus to the building. Using these maps one describes a G(K) invariant pure affinoid covering of the set of stable points. The reduction of the affinoid covering is given.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      On the action of the unitary group on the projective plane over a local field
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      On the action of the unitary group on the projective plane over a local field
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      On the action of the unitary group on the projective plane over a local field
      Available formats
      ×
Copyright
References
Hide All
[1]Bosch, S., Güntzer, U. and Remmert, R., Non-archimedean analysis (Springer, Berlin, 1984).
[2]Fresnel, J. and van der Put, M., Geométrie analytique rigide et applications, Prog. Math. 18 (Birkhäuser, Boston, 1981).
[3]Bruhat, F. and Tits, J., ‘Groupes Réductifs sur un corps local I: Données radicielles valuées’, Inst. Hautes Études Sci. Publ. Math. 41 (1972), 5251.
[4]van der Put, M. and Voskuil, H., ‘Symmetric spaces associated to split algebraic groups over a local field’, J. ReineAngew. Math. 433 (1992), 69100.
[5]Mustafin, G. A., ‘Nonarchimedean uniformization’, Math. USSR-Sb. 34 (1978), 187214.
[6]Oda, T., Convex bodies and algebraic geometry (Springer, Berlin, 1988).
[7]Tits, J., ‘Reductive groups over local fields’, Proc. Amer. Math. Soc. Symp. Pure Math. 33 (1979), 2969.
[8]Voskuil, H., Non-archimedean Hopf Surfaces, Séminaire de Théorie des Nombres de Bordeaux 3(1991), 405466.
[9]Voskuil, H., ‘P-adic symmetric spaces: The unitary group acting on the projective plane’, in: Algebraic geometry symposium at Kinosaki, 1993 (ed. profMaruyama, ) (Kyoto University Press, Kyoto, 1994), pp. 5876.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

MSC classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed