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C2 building and projective space

Part of: Linear algebraic groups and related topics Special varieties Non-Archimedean analysis

Published online by Cambridge University Press:  09 April 2009

K. F. Lai
K. F. Lai
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia
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Abstract

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We study the stability map from the rigid analytic space of semistable points in P3 to convex sets in the building of Sp2 over a local field and construct a pure affinoid covering of the space of stable points.

MSC classification

Secondary: 14M17: Homogeneous spaces and generalizations 32P05: Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem) 20G25: Linear algebraic groups over local fields and their integers
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 76 , Issue 3 , June 2004 , pp. 383 - 402
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Bosch, S., Günther, U. and Remmert, R., Non-archimedian analysis (Springer, New York, Basel, 1984).CrossRefGoogle Scholar
[2]Fernel, J. and Van der Put, M., Géométrie analytique rigide et applications, Progress in Math. 18 (Birkhäuser, 1981).Google Scholar
[3]Flaschka, H. and Haine, L., ‘Torus orbits in G/P’, Pacific J. Math. 149 (1991), 251–292.CrossRefGoogle Scholar
[4]Goldman, O. and Iwahori, N., ‘The space of p-adic norms’, Acta Math. 109 (1963), 137–177.CrossRefGoogle Scholar
[5]Hsia, L.-C., ‘A weak Néron model with applications to p-adic dynamical systems’, Compositio Math. 100 (1996), 277–304.Google Scholar
[6]Iversen, B., ‘The geometry ofr algebraic groups’ Adv. Math. 20 (1976), 57–85.CrossRefGoogle Scholar
[7]Kempf, G. R., ‘Linear systems on homogeneour spaces’, Ann. of Math. 103 (1976), 557–591.CrossRefGoogle Scholar
[8]Kurihara, A., ‘Construction of p-adic unit balls and the Hirzebruch proportionality’ Amer. J. Math. 102 (1980), 565–648.CrossRefGoogle Scholar
[9]Moy, A., ‘Displacement functions in Bruhat-Tits buildings’, Proc. Sympos. Pure Math. 68 (2000), 483–500.CrossRefGoogle Scholar
[10]Mumford, D., ‘An analytic construction of degenerating curves over complete local rings’, Compositio Math. 24 (1972), 129–174.Google Scholar
[11]Mumford, D., Fogarty, J. and Kirwan, F., Geometric invariant theory (Springer, New York, 1994).CrossRefGoogle Scholar
[12]van der Put, M. and Voskuil, H., ‘Symmetric space associated to split algebraic groups over a local field’, J. Reine Angew. Math. 433 (1992), 69–100.Google Scholar
[13]Rapoport, M., ‘Period domains over finite and local fields’, Proc. Sympos. Pure Math. 62–1 (1997), 361–381.CrossRefGoogle Scholar
[14]Schneider, P. and Stuhler, U., ‘The cohomology of p-adic symmetric spaces’, Invent. Math. 105 (1991), 47–122.CrossRefGoogle Scholar
[15]Tits, J., ‘Reductive groups over local fields’, Proc. Sympos. Pure Math. 33 (1979), 29–69.CrossRefGoogle Scholar
[16]Voskuil, H., ‘On the action of the unitary group on the projective plane over a local field’, J. Austral. Math. Soc. (Series A) 62 (1997), 371–397.CrossRefGoogle Scholar