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Palabras claves o descriptores: RATIONAL POINT (Comienzo)
2 registros cumplieron la condición especificada en la base de información BIBCYT. ()
Registro 1 de 2, Base de información BIBCYT
Publicación seriada
Referencias AnalíticasReferencias Analíticas
Autor: Esnault, Héléne ; Chenyang, Xu
Título: Congruence for rational points over finite fields and coniveau over local fields
Páginas/Colación: pp. 2679-2688
Fecha: May 2009
Transactions of the American Mathematical Society Vol. 361, no.5 May 2009
Información de existenciaInformación de existencia

Palabras Claves: Palabras: CONGRUENCE CONGRUENCE, Palabras: CONIVEAU CONIVEAU, Palabras: RATIONAL POINT RATIONAL POINT

Resumen
For about twenty five years it was a kind of folk theorem that complex vector-fields defined on (with open set in ) by

If the $ \ell$-adic cohomology of a projective smooth variety, defined over a local field $ K$with finite residue field $ k$, is supported in codimension $ \ge 1$, then every model over the ring of integers of $ K$has a $ k$-rational point. For $ K$a $ p$-adic field, this is proved in (Esnault, 2007, Theorem 1.1). If the model $ \mathcal{X}$is regular, one has a congruence $ \vert\mathcal{X}(k)\vert\equiv 1 $modulo $ \vert k\vert$for the number of $ k$-rational points (Esnault, 2006, Theorem 1.1). The congruence is violated if one drops the regularity assumption.

Registro 2 de 2, Base de información BIBCYT
Publicación seriada
Referencias AnalíticasReferencias Analíticas
Autor: Goodwin, Simon M. ; Röhrle, Gerard
Título: Rational points on generalized flag varieties and unipotent conjugacy in finite groups of Lie type
Páginas/Colación: pp. 177-206
Fecha: January 2009
Transactions of the American Mathematical Society Vol. 361, no. 1 January 2009
Información de existenciaInformación de existencia

Palabras Claves: Palabras: FINITE GROUPS FINITE GROUPS, Palabras: RATIONAL POINTS RATIONAL POINTS

Resumen
It is proved herein that any absolute minimizer for a suitable Hamiltonian is a viscosity solution of the Aronsson equation:

Let $ G$be a connected reductive algebraic group defined over the finite field $ \mathbb{F}_q$, where $ q$is a power of a good prime for $ G$. We write $ F$for the Frobenius morphism of $ G$corresponding to the $ \mathbb{F}_q$-structure, so that $ G^F$is a finite group of Lie type. Let $ P$be an $ F$-stable parabolic subgroup of $ G$and let $ U$be the unipotent radical of $ P$. In this paper, we prove that the number of $ U^F$-conjugacy classes in $ G^F$is given by a polynomial in $ q$, under the assumption that the centre of $ G$is connected. This answers a question of J. Alperin (2006).

In order to prove the result mentioned above, we consider, for unipotent $ u \in G^F$, the variety $ \mathcal{P}^0_u$of $ G$-conjugates of $ P$whose unipotent radical contains $ u$. We prove that the number of $ \mathbb{F}_q$-rational points of $ \mathcal{P}^0_u$is given by a polynomial in $ q$with integer coefficients. Moreover, in case $ G$is split over $ \mathbb{F}_q$and $ u$is split (in the sense of T. Shoji, 1987), the coefficients of this polynomial are given by the Betti numbers of $ \mathcal{P}^0_u$. We also prove the analogous results for the variety $ \mathcal{P}_u$consisting of conjugates of $ P$that contain $ u$.

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

UCLA - Biblioteca de Ciencias y Tecnologia Felix Morales Bueno

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