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LARGE SCHUBERT VARIETIES
, 1999
"... For a semisimple adjoint algebraic group G and a Borel subgroup B, consider the double classes BwB in G and their closures in the canonical compactification of G: we call these closures large Schubert varieties. We show that these varieties are normal and CohenMacaulay; we describe their Picard gr ..."
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Cited by 5 (4 self)
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For a semisimple adjoint algebraic group G and a Borel subgroup B, consider the double classes BwB in G and their closures in the canonical compactification of G: we call these closures large Schubert varieties. We show that these varieties are normal and CohenMacaulay; we describe their Picard group and the spaces of sections of their line bundles. As an application, we construct geometrically van der Kallen’s filtration of the algebra of regular functions on B. We also construct a degeneration of the flag variety G/B embedded diagonally in G/B ×G/B, into a union of Schubert varieties. This leads to formulae for the class of the diagonal in Tequivariant Ktheory of G/B × G/B, where T is a maximal torus of B.
RESTRICTED INFINITESIMAL DEFORMATIONS OF RESTRICTED SIMPLE LIE ALGEBRAS
, 705
"... Abstract. We compute the restricted infinitesimal deformations of the restricted simple Lie algebras over an algebraically closed field of characteristic p ≥ 5. 1. ..."
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Abstract. We compute the restricted infinitesimal deformations of the restricted simple Lie algebras over an algebraically closed field of characteristic p ≥ 5. 1.
DEFORMATIONS OF SIMPLE FINITE GROUP SCHEMES
, 705
"... Abstract. Simple finite group schemes over an algebraically closed field of positive characteristic p ̸ = 2, 3 have been classified. We consider the problem of determining their infinitesimal deformations. In particular, we compute the infinitesimal deformations of the simple finite group schemes of ..."
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Abstract. Simple finite group schemes over an algebraically closed field of positive characteristic p ̸ = 2, 3 have been classified. We consider the problem of determining their infinitesimal deformations. In particular, we compute the infinitesimal deformations of the simple finite group schemes of height one corresponding to the restricted simple Lie algebras. 1.
LIFTING DMODULES FROM POSITIVE TO ZERO CHARACTERISTIC
, 2011
"... Abstract. — We study liftings or deformations of Dmodules (D is the ring of differential operators from EGA IV) from positive characteristic to characteristic zero using ideas of Matzat and Berthelot’s theory of arithmetic Dmodules. We pay special attention to the growth of the differential Galoi ..."
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Abstract. — We study liftings or deformations of Dmodules (D is the ring of differential operators from EGA IV) from positive characteristic to characteristic zero using ideas of Matzat and Berthelot’s theory of arithmetic Dmodules. We pay special attention to the growth of the differential Galois group of the liftings. We also apply formal deformation theory (following Schlessinger and Mazur) to analyze the space of all liftings of a given Dmodule in positive characteristic. At the end we compare the problems of deforming a Dmodule with the problem of deforming a representation of a naturally associated group scheme. Résumé (Relèvement de Dmodules de caractéristique positive en caractéristique nulle) Nous étudions des relèvements des Dmodules (D est l’anneau des opérateurs différentiels de EGA IV) de la caractéristique positive en caractéristique nulle en utilisant des idées de Matzat et la théorie de descente par Frobenius (pour les Dmodules arithmétiques) de Berthelot. Nous prêtons une attention particulière à la croissance du groupe de Galois différentiel du relèvement. Nous appliquons aussi la théorie locale
THE CONE OF EFFECTIVE ONE–CYCLES OF CERTAIN G–VARIETIES
, 2002
"... Abstract. Let X be a normal projective variety admitting an action of a semisimple group with a unique closed orbit. We construct finitely many rational curves in X, all having a common point, such that every effective one–cycle on X is rationally equivalent to a unique linear combination of these c ..."
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Abstract. Let X be a normal projective variety admitting an action of a semisimple group with a unique closed orbit. We construct finitely many rational curves in X, all having a common point, such that every effective one–cycle on X is rationally equivalent to a unique linear combination of these curves with non–negative rational coefficients. When X is nonsingular, these curves are projective lines, and they generate the integral Chow group of one–cycles.