Javier López Peña
Projective geometry for blueprints.
Fri, 03/09/2012 - 15:01 — SomNambulAuthors: Javier López Peña, Oliver Lorscheid
Subjects: Algebraic Geometry
AbstractIn 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).- 4 comments
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On the classification of twisting maps between $K^n$ and $K^m$.
Sat, 09/26/2009 - 04:10 — SomNambulAuthors: Javier López Peña, Gabriel Navarro, Pascual Jara, Dragoş Ştefan
Subjects: Rings and Algebras
AbstractWe define the notion of admissible pair for an algebra $A$, consisting on a
couple $(\Gamma,R)$, where $\Gamma$ is a quiver and $R$ a unital, splitted and
factorizable representation of $\Gamma$, and prove that the set of admissible
pairs for $A$ is in one to one correspondence with the points of the variety of
twisting maps $\mathcal{T}_A^n:=\mathcal{T}(K^n,A)$. We describe all these
representations in the case $A=K^m$.Mapping F_1-land:An overview of geometries over the field with one element.
Wed, 09/02/2009 - 12:02 — SomNambulAuthors: Javier López Peña, Oliver Lorscheid
Subjects: Algebraic Geometry
AbstractThis 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.
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