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About Hrushovski and Loeser's work on the homotopy type of Berkovich spaces
Those are the notes of the two talks I gave in april 2013 in St-John (US
Virgin Islands) during the Simons Symposium on non-Archimedean and tropical
geometry. They essentially consist of a survey of Hrushovski and Loeser's work
on the homotopy type of Berkovich spaces; the last section explains how the
author has used their work for studying pre-image of skeleta.Comment: 31 pages. This text will appear in the Proceedings Book of the Simons
Symposium on non-Archimedean and tropical geometry (april 2013, US Virgin
Islands). I've taken into account the remarks and suggestion of the referee
Mixed Crop Livestock Farming Incorporating Agroforestry Orchards Facing the New Cap
In the context of the new CAP, decoupling subsidies from production should incite farmers to reorganize their production systems, particularly through diversification opportunities. In this paper we focus our analysis on the conditions that could permit the development of extensive orchards by modelling mixed crop livestock farms, which incorporate orchards. A mathematical programming model is built to simulate various intensification levels characterizing different technical pathways within the different farm activities (cattle breeding, forage fields, arboriculture). This model also enables us to take into account some environmental indicators related to these pathways. Moreover, the method illustrates technical complementarities existing within the diversified systems, thanks to the joint production phenomena introduced into our analysis. We show how these complementarities can be integrated into the farmer's decision criteria.decoupling, diversification, agroforestry orchards, joint production, mathematical programming, Agribusiness, C61, D24, Q12, Q21,
Triangulation et cohomologie \'{e}tale sur une courbe analytique
Let be a non-archimedean complete valued field and let X be a smooth
Berkovich analytic -curve. Let be a finite locally constant \'{e}tale
sheaf on whose torsion is prime to the residue characteristic. We denote by
the underlying topological space and by the canonical map from the
\'{e}tale site to . In this text we define a triangulation of , we show
that it always exists and use it to compute and
. If is the analytification of an algebraic
curve we give sufficient conditions so that those groups are isomorphic to
their algebraic counterparts ; if the cohomology of has a dualizing sheaf
in some degree (e.g is -adic, or ) then we prove a duality
theorem between and where is the tensor product of the dual sheaf of
with the dualizing sheaf and the sheaf of -th roots of unity
Les espaces de Berkovich sont excellents
In this paper, we first study the local rings of a Berkovich analytic space
from the point of view of commutative algebra. We show that those rings are
excellent ; we introduce the notion of a an analytically separable extension of
non-archimedean complete fields (it includes the case of the finite separable
extensions, and also the case of any complete extension of a perfect complete
non-archimedean field) and show that the usual commutative algebra properties
(Rm, Sm, Gorenstein, Cohen-Macaulay, Complete Intersection) are stable under
analytically separable ground field extensions; we also establish a GAGA
principle with respect to those properties for any finitely generated scheme
over an affinoid algebra.
A second part of the paper deals with more global geometric notions : we
define, show the existence and establish basic properties of the irreducible
components of analytic space ; we define, show the existence and establish
basic properties of its normalization ; and we study the behaviour of
connectedness and irreducibility with respect to base change.Comment: This is the (almost) definitive version of the paper, which is going
to appear in "Annales de l'institut Fourier
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