CONTOU CARRERE Carlos
Carlos.CONTOU-CARRERE
umontpellier.fr
0467143556
Bureau: 402, Etg: 1, Bât: 13 - Site : Campus Triolet
Domaines de Recherche: - Mathématiques/Géométrie algébrique [math.AG]
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Productions scientifiques :
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Buildings and Schubert Schemes 
Auteur(s): Contou-Carrere C.
Ouvrage: CRC Press (2016) 462p.
Ref HAL: hal-01940773_v1
Exporter : BibTex | endNote
Résumé: The first part of this book introduces the Schubert Cells and varieties of the general linear group Gl (k^(r+1)) over a field k according to Ehresmann geometric way. Smooth resolutions for these varieties are constructed in terms of Flag Configurations in k^(r+1) given by linear graphs called Minimal Galleries. In the second part, Schubert Schemes, the Universal Schubert Scheme and their Canonical Smooth Resolution, in terms of the incidence relation in a Tits relative building are constructed for a Reductive Group Scheme as in Grothendieck's SGAIII. This is a topic where algebra and algebraic geometry, combinatorics, and group theory interact in unusual and deep ways.
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Jacobienne locale d'une courbe formelle relative
Auteur(s): Contou-Carrere C.
(Article) Publié:
Rendiconti Del Seminario Matematico Della Università Di Padova, vol. 130 p.1–106 (2013)
Texte intégral en Openaccess : 
Ref HAL: hal-01286493_v1
DOI: 10.4171/RSMUP/130-1
Exporter : BibTex | endNote
7 citations
Résumé: This article is devoted to the proof of a relative duality formula on a noetherian scheme $S$, giving rise on the spectrum of a field$S=Spec\,k$ to local symbols of class field theory. Relative local symbols are obtained in terms of the universal property of a couple $(\mathfrak{J},f)$, of a $S$-group functor $\mathfrak{J}$, associated to a $S$-formal curve $\mathfrak{X}$locally of the form $\mathfrak{X}=Spf\, A[[T]]$ ($S=Spec\,A)$. $\mathfrak{J}$ is a $S$-group extension of the completion $\check{W}$ of the universal $S$-Witt vectors group $W$, by the group of units $\mathcal{O}_{S}[[T]]^{*}$. We associate an $S$-functor $\mathfrak{J}_{omb}$to $\mathfrak{J}$, and we define an Abel-Jacobi morphism $f:\mathfrak{U}=Spec\ A[[T]][T^{-1}]\longrightarrow \mathfrak{J}_{omb}$ , setting up a group isomorphism:$$Hom_{S-gr}(\mathfrak{J},G)\simeq G(\mathfrak{U}),$$where $G$ denotes a commutative smooth $S$-group scheme.We define an $S$-bihomomorphism$$\mathfrak{J}\times\mathfrak{J}\longrightarrow\mathbb{G}_{m},$$which is a local symbol (The Tame Symbol), identifying $\mathfrak{J}$ to its own Cartier dual group $\check{\mathfrak{J}}=\underline{Hom}_{S-gr}(\mathfrak{J},\mathbb{G}_{m})$, and inducing the above isomorphism for $G=\mathbb{G}_{m}$. It follows that $\mathfrak{J}$ may be interpreted as the relative Loop Group: $$\underline{\mathbb{G}}_{m}(\mathfrak{U}):S'\longrightarrow G(\mathfrak{U}_{\{S'\}})\ ,$$$S'=Spec\ A'$ denotes a $S$-scheme, and we write $\mathfrak{U}_{\{S'\}}=Spec\ A'[[T]][T^{-1}]$, and as the $A$-universal group of Witt-Bivectors.\\The couple $(\mathfrak{J},f)$ may be seen as the local analogue of the relative Rosenlicht Jacobian (Generalized Jacobian) defined by a $S$-smooth curve $X$.
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Equivariant resolutions of Shubert varieties.
Auteur(s): Contou-Carrere C.
Conférence invité: Workshop on singularities (Trieste, IT, 2007-06-15)
Ref HAL: hal-00285138_v1
Exporter : BibTex | endNote
Résumé: We give a combinatorial method for the construction of a family of resolutions for general Schubert varieties.This resolution is equivariant relatively to the parabolic subgroup defining a given Schubert variety.
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