Главная

Oliver Lorscheid

  1. Projective geometry for blueprints.

    Пт, 03/09/2012 - 15:01 — SomNambul
    Authors: Javier López Peña, Oliver Lorscheid
    Subjects: Algebraic Geometry
    Abstract

    In this note, we generalize the Proj-construction from usual schemes to blue
    schemes. This yields the definition of projective space and projective
    varieties over a blueprint. In particular, it is possible to descend closed
    subvarieties of a projective space to a canonical F_1-model. We discuss this
    explicitly in case of the Grassmannian Gr(2,4).

  2. The geometry of blueprints. Part II: Tits-Weyl models of algebraic groups.

    Пнд, 01/09/2012 - 15:01 — SomNambul
    Authors: Oliver Lorscheid
    Subjects: Algebraic Geometry
    Abstract

    This paper is dedicated to a problem raised by Jacquet Tits in 1956: the Weyl
    group of a Chevalley group should find an interpretation as a group over what
    is nowadays called $\mathbb{F}_1$, \emph{the field with one element}. Based on
    Part I of The geometry of blueprints, we introduce the class of \emph{Tits
    morphisms} between blue schemes. The resulting \emph{Tits category}
    $\textup{Sch}_\mathcal{T}$ comes together with a base extension to (semiring)
    schemes and the so-called \emph{Weyl extension} to sets.

  3. Graphs of Hecke operators.

    Пт, 12/17/2010 - 16:01 — SomNambul
    Authors: Oliver Lorscheid
    Subjects: Number Theory
    Abstract

    Let $X$ be a curve over $\F_q$ with function field $F$. In this paper, we
    define a graph for each Hecke operator with fixed ramification. A priori, these
    graphs can be seen as a convenient language to organize formulas for the action
    of Hecke operators on automorphic forms. However, they will prove to be a
    powerful tool for explicit calculations and proofs of finite dimensionality
    results.

  4. Mapping F_1-land:An overview of geometries over the field with one element.

    Ср, 09/02/2009 - 12:02 — SomNambul
    Authors: Javier López Peña, Oliver Lorscheid
    Subjects: Algebraic Geometry
    Abstract

    This paper gives an overview of the various approaches towards F_1-geometry.
    In a first part, we review all known theories in literature so far, which are:
    Deitmar's F_1-schemes, To\"en and Vaqui\'e's F_1-schemes, Haran's F-schemes,
    Durov's generalized schemes, Soul\'e's varieties over F_1 as well as his and
    Connes-Consani's variations of this theory, Connes and Consani's F_1-schemes,
    the author's torified varieties and Borger's Lambda-schemes.

Math-arch

RSS-материал