Conjugates of shimura varieties

Milne, J. S.; Shih, K.-Y.

doi:10.1007/bfb0091633

Cited by 18 publications

(66 citation statements)

References 10 publications

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“…Si Y(T ′′ ) désigne le groupe de co-caractères d'un tore T ′′ , cette dernière condition est en faitéquivalentè a la surjectivité de l'application Y(T ) → Y(T ). La construction suivante, dite d'une zextension de G, est un cas particulier de [MS,Prop. 3.1].…”

Section: Ecrivons Maintenant Hunclassified

Un Scindage Du Morphisme De Frobenius Sur L’algèbre Des Distributions D’un Groupe Réductif

Gros

Kaneda

2019

The Quarterly Journal of Mathematics

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Pour un groupe algébrique semi-simple simplement connexe sur un corps algébriquement clos de caractéristique positive, nous avons précédemment construit un scindage de l'endomorphisme de Frobenius sur son algèbre des distributions. Nous généralisons la construction au cas de des groupes réductifs et en dégageons les corollaires correspondants.For a simply connected semisimple algebraic group over an algebraically closed field of positive characteristic we have already constructed a splitting of the Frobenius endomorphism on its algebra of distributions. We generalize the construction to the case of general reductive groups and derive the corresponding corollaries.

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Section: Ecrivons Maintenant Hunclassified

Un Scindage Du Morphisme De Frobenius Sur L’algèbre Des Distributions D’un Groupe Réductif

Gros

Kaneda

2019

The Quarterly Journal of Mathematics

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“…11 The authors found [39,40] and [41] useful in learning Shimura variety, connected Shimura variety, and Mumford-Tate group, respectively. 12 For an extension field E over F , Res E/F (G m ) is an Abelian group identical to E × = E\{0}.…”

Section: André-oort Conjecture and Coleman-oort Conjecturementioning

confidence: 99%

“…In this article, we just simply ignore this subtlety by tensoring Q. 39 We only consider Abelian varieties with a principal polarization in this article.…”

Section: Complex Multiplication On a Simple Abelian Varietymentioning

confidence: 99%

Revisiting arithmetic solutions to theW=0condition

Kanno

Watari

2017

Phys. Rev. D

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The gravitino mass is expected not to be much smaller than the Planck scale for a large fraction of vacua in flux compactifications. There is no continuous parameter to tune even by hand, and it seems that the gravitino mass can be small only as a result of accidental cancellation among period integrals weighted by integer-valued flux quanta. DeWolfe et.al. (2005) proposed to pay close attention to vacua where the Hodge decomposition is possible within a number field, so that the precise cancellation takes place as a result of algebra. We focus on a subclass of those vacua-those with complex multiplications-and explore more on the idea in this article. It turns out, in Type IIB compactifications, that those vacua admit non-trivial supersymmetric flux configurations if and only if the reflex field of the Weil intermediate Jacobian is isomorphic to the quadratic imaginary field generated by the axidilaton vacuum expectation value. We also found that flux statistics is highly enriched on such vacua, as F-term conditions become linearly dependent.

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“…For a general G, choose a central extension ν : H → G such that H der is simply-connected, and S := Ker(ν) is a split torus (see [MS,Prop. 3.1]).…”

Section: A1 Proof Of Lemma 22mentioning

confidence: 99%

Moduli spaces of principal F-bundles

Varshavsky

2004

Sel. math., New ser.

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In this paper we construct certain moduli spaces, which we call moduli spaces of (principal) F -bundles, and study their basic properties. These spaces are associated to triples consisting of a smooth projective geometrically connected curve over a finite field, a split reductive group G, and an irreducible algebraic representation ω of ( G) n /Z( G). Our spaces generalize moduli spaces of F -sheaves, studied by Drinfeld and Lafforgue, which correspond to the case G = GLr and ω is the tensor product of the standard representation and its dual. The importance of the moduli spaces of F -bundles is due to the belief that Langlands correspondence is realized in their cohomology.

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Conjugates of shimura varieties

Abstract: This is an introduction to the theory of Shimura varieties, or, in other words, to the arithmetic theory of automorphic functions and holomorphic automorphic forms.

Cited by 18 publications

References 10 publications

Un Scindage Du Morphisme De Frobenius Sur L’algèbre Des Distributions D’un Groupe Réductif

Un Scindage Du Morphisme De Frobenius Sur L’algèbre Des Distributions D’un Groupe Réductif

Revisiting arithmetic solutions to theW=0condition

Moduli spaces of principal F-bundles

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