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Extensions panachées autoduales

Published online by Cambridge University Press:  06 March 2013

Daniel Bertrand*
Affiliation:
Institut de Mathématiques de [email protected]
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Abstract

We study self-duality of Grothendieck's blended extensions in the context of a tannakian category. The set of equivalence classes of symmetric, resp. antisymmetric, blended extensions is naturally endowed with a torsor structure, which enables us to compute the unipotent radical of the associated monodromy groups in various situations.

Type
Research Article
Copyright
Copyright © ISOPP 2013 

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References

Références

BK.Barbieri-Viale, L., Kahn, B.: On the derived category of 1-motives; arXiv : math.AG 1009.1900 (voir aussi Prépubl. Math. IHÉS, M/07/22, Juin 2007).Google Scholar
Be.Bertolin, C. : Le radical unipotent du groupe de Galois motivique d'un 1-motif; Math. Ann. 327 (2003), 585607.Google Scholar
B1.Bertrand, D. : Relative splittings of one-motives; Contemp. Maths 210 (1998), 317Google Scholar
B2.Bertrand, D. : Unipotent radicals of differential Galois groups; Math. Ann. 321 (2001), 645666.CrossRefGoogle Scholar
B3.Bertrand, D. : Extensions panachées et dualité; Prépublications de l'Institut de Mathématiques de Jussieu, No 287, Avril 2001 (non publié).Google Scholar
B4.Bertrand, D. : Special points and Poincaré bi-extensions; with an Appendix by Edixhoven, Bas; arXiv : math.NT 1104.5178v1Google Scholar
Bo.Borel, A. : Linear algebraic groups; PSPM AMS, vol. 9 (1966), 319.Google Scholar
Br.Breen, L. : Biextensions alternées; Compo. Math. 63 (1987), 99122.Google Scholar
By.Brylinski, J-L. : 1-motifs et formes automorphes; Publ. Math. Univ. Paris 7 15 (1983), 43106.Google Scholar
D.Deligne, P. : Théorie de Hodge III; Publ. Math. IHES 44 (1975), 577.Google Scholar
DM.Deligne, P., Milne, J.: Tannakian categories; Springer LN 900 (1982), 101228.Google Scholar
G.Grothendieck, A. : Modèles de Néron et monodromie; SGA VII.1, no 9, Springer LN 288 (1968).Google Scholar
H.Hardouin, C. : Calcul du groupe de Galois différentiel du produit de trois opérateurs complètement réductibles; CRAS Paris 341 (2005), 349352.Google Scholar
K.Kahn, B. : Représentations orthogonales et symplectiques sur un corps de caractéristique différente de 2; Comm. in Algebra 31 (2003), 133196.Google Scholar
M.Milne, J.: Canonical models of (mixed) Shimura varieties and automorphic vector bundles; “Automorphic forms, Shimura varieties and L-functions”, I,; Perspect. Maths 10 (1990), 283411. Academic Press.Google Scholar
RSZ.Ramis, J-P., Sauloy, J., Zhang, C. : Local analytic classification of q-difference equations; arXiv : math.AQ 0903.0853 (à paraître dans Astérisque).Google Scholar
R.Ribet, K. : Cohomological realization of a family of one-motives; J. Number Th. 25 (1987), 152161.Google Scholar
Sh.Shimura, G. : Euler products and Eisenstein series; CBMS Regional Conference Series in Maths 93 (1997), AMS.Google Scholar