On the supersingular loci of quaternionic Siegel space

• Oliver Bültel ^[1]
  1. [1] Universität Duisburg-Essen Mathematische Fakultät
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 16, Nº. 3, 2014, págs. 67-85
• Idioma: inglés
• DOI: 10.4067/S0719-06462014000300006
• Enlaces
  • Texto completo
• Resumen
  • español

    El artículo estudia el lugar supersingular del espacio modulo característico p de abeliano polarizado 8-veces principal que son equipados con una acción de un orden maximal en un ólgebra quaterniona, que es no-divisible en ∞, pero se divide en p. El principal resultados es que los componentes irreducibles son superficies de Fermat de grado p +1.

  • English

    The paper studies the supersingular locus of the characteristic p moduli space of principally polarized abelian 8-folds that are equipped with an action of a maximal order in a quaternion algebra, that is non-split at ∞ but split at p. The main result is that its irreducible components are Fermat surfaces of degree p + 1.

• Referencias bibliográficas
  • Bültel, O. (1999). Rational Points on some PEL-stacks. manuscripta math. 99. 395-410
  • Bültel, O. (2002). The congruence relation in the non-PEL case. J. reine angew. Math. 544. 133-159
  • Grothendieck, A. (1970). Groupes de Barsotti-Tate et cristaux de Dieudonné. Sém. Math. Sup. 45.
  • Hartshorne, R. (1977). Algebraic Geometry. Springer Verlag. New York.
  • Katsura, T,Oort, F. (1987). Families of supersingular abelian surfaces. Compos. Math. 62. 107-167
  • Kottwitz, R. (1992). Points on some Shimura varieties over finite fields. Journal of the AMS. 5. 373-444
  • Kraft, H. (1975). Kommutative algebraische p-Gruppen: Sonderforschungsbereich Theoretische Mathematik. Universitiät Bonn.
  • Li, K-Z. (1989). Classification of Supersingular Abelian Varieties. Math. Ann. Band. 283. 333-351
  • Li, K-Z,Oort, F. (1998). Moduli of Supersingular Abelian Varieties. Lecture Notes in Mathematics. 1680.
  • Manin, Y. (1963). The theory of commutative formal groups over fields of positive characteristic. Russ. Math. Surveys. 18. 1-80
  • Moonen, B. (2001). Group Schemes with Additional Structures and Weyl Group Cosets. Moduli of Abelian Varieties. 195. 255-298
  • Oda, T,Oort, F,Nagata. (1977). Supersingular abelian varieties. Intl. Sympos. on Algebraic Geometry. Kyoto.
  • Ogus, A. (1989). Absolute Hodge Cycles and Crystalline Cohomology. Hodge Cycles, Motives, and Shimura varieties. 900. 357-414
  • Oort, F. (1991). Hyperelliptic supersingular curves. Arithmetic Algebraic Geometry, Texel. 89. 247-284
  • Richartz, M. (1998). Klassifikation von selbstdualen Dieudonnégittern in einem dreidimensionalen polarisierten supersingulärem Isokristall.
  • Scharlau, W. (1985). Quadratic and Hermitian Forms. 270.
  • Zink, T. (2002). The display of a formal p-divisible Group. Cohomologies p-adiques et Applications Arithmetiques (I). 278. 127-248