Arithmetic infinite Grassmannians and the induced central extensions

• Francisco J. Plaza Martín
  1. [1] Universidad de Salamanca

     Universidad de Salamanca

     Salamanca, España

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 61, Fasc. 1, 2010, págs. 107-129
• Idioma: inglés
• DOI: 10.1007/bf03191229
• Enlaces
  • Texto completo
• Dialnet Métricas: 1 Cita
• Resumen

  • The construction of families of Sato Grassmannians, their determinant line bundles and the extensions induced by them are given. The base scheme is an arbitrary scheme.

• Referencias bibliográficas
  • G.W. Anderson and F. Pablos Romo, Simple proofs of classical explicit reciprocity laws on curves using determinant groupoids over an Artinian...
  • A. Álvarez Vázquez, J.M. Muñoz Porras, and F.J. Plaza Martín, The algebraic formalism of soliton equation over arbitrary base fields, in Workshop...
  • A. Beilinson, S. Bloch, and H. Esnault, ε-factors for Gauss-Manin determinants, Dedicated to Yuri I. Manin on the occasion of his 65th birthday,...
  • M.J. Bergvelt, Infinite super Grassmannians and super Plücker equations, in Infinite-dimensional Lie algebras and groups (Luminy-Marseille,...
  • C. Contou-Carrère, Jacobienne locale, groupe de bivecteurs de Witt universel, et symbole modéré, C. R. Acad. Sci. Paris Sér. I 318 (1994),...
  • E. Date, M. Jimbo, M. Kashiwara, and T. Miwa, Transformation groups for soliton equations, Nonlinear integrable systems—classical theory and...
  • A. Grothendieck, Éléments de géométrie algébrique I, Le Langage des schémas, Inst. Hautes Études Sci. Publ. Math. 4 (1960), 288.
  • E. Frenkel, Lectures on the Langlands program and conformal field theory, Frontiers in Number Theory, Physics, and Geometry II, 387–533, Springer,...
  • R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics 52, Springer-Verlag, New York-Heidelberg, 1977.
  • D. Hernández Serrano, J.M. Muñoz Porras, and F.J. Plaza Martín, Higgs pairs and Infinite Grassmannian, Int. J. Math., to appear.
  • V.G. Kac and A.K. Raina, Bombay Lectures on Highest Weight Representations of Infinite-Dimensional Lie Algebras, Advanced Series in Mathematical...
  • N. Kawamoto, Y. Namikawa, A. Tsuchiya, and Y. Yamada, Geometric realization of conformal field theory on Riemann surfaces, Comm. Math. Phys....
  • F. Knudsen and D. Mumford, The projectivity of the moduli space of stable curves I: preliminaries on det and div, Math. Scand. 39 (1976),...
  • J. Leech, Extending groups by monoids, J. Algebra 74 (1982), 1–19.
  • M. Mulase, Cohomological structure in soliton equations and Jacobian varieties, J. Differential Geom. 19 (1984), 403–430.
  • M. Mulase and J.M. Rabin, Super Krichever functor, Internat. J. Math. 2 (1991), 741–760.
  • J.M. Muñoz Porras and F. Pablos Romo, Generalized reciprocity laws, Trans. Amer. Math. Soc. 360 (2008), 3473–3492.
  • J.M. Muñoz Porras and F.J. Plaza Martín, Equations of the moduli space of pointed curves in the infinite Grassmannian, J. Differential Geom....
  • J.M. Muñoz Porras and F.J. Plaza Martín, Automorphism group of k((t)): applications to the bosonic string, Comm. Math. Phys. 216 (2001), 609–634.
  • I. Quandt, On a relative version of the Krichever correspondence, Bayreuth. Math. Schr. 52 (1997), 1–74.
  • G. Segal and G. Wilson, Loop groups and equations of KdV type, Inst. Hautes Études Sci. Publ. Math. 61 (1985), 5–65.
  • M. Sato and Y. Sato, Soliton equations as dynamical systems on infinite-dimensional Grassmann manifold, Nonlinear Partial Differential Equations...
  • T. Shiota, Characterization of Jacobian varieties in terms of soliton equations, Invent. Math. 83 (1986), 333–382.
  • E. Witten, Quantum field theory, Grassmannians, and algebraic curves, Comm. Math. Phys. 113 (1988), 529–600.