Mumford-Tate groups of mixed Hodge structures and the theorem of the fixed part

Yves André

Compositio Mathematica (1992)

  • Volume: 82, Issue: 1, page 1-24
  • ISSN: 0010-437X

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André, Yves. "Mumford-Tate groups of mixed Hodge structures and the theorem of the fixed part." Compositio Mathematica 82.1 (1992): 1-24. <http://eudml.org/doc/90145>.

@article{André1992,
author = {André, Yves},
journal = {Compositio Mathematica},
keywords = {theorem of the fixed part; variation of mixed Hodge structure; Mumford- Tate group; abelian integrals},
language = {eng},
number = {1},
pages = {1-24},
publisher = {Kluwer Academic Publishers},
title = {Mumford-Tate groups of mixed Hodge structures and the theorem of the fixed part},
url = {http://eudml.org/doc/90145},
volume = {82},
year = {1992},
}

TY - JOUR
AU - André, Yves
TI - Mumford-Tate groups of mixed Hodge structures and the theorem of the fixed part
JO - Compositio Mathematica
PY - 1992
PB - Kluwer Academic Publishers
VL - 82
IS - 1
SP - 1
EP - 24
LA - eng
KW - theorem of the fixed part; variation of mixed Hodge structure; Mumford- Tate group; abelian integrals
UR - http://eudml.org/doc/90145
ER -

References

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  1. [A1] André, Y., Sur certaines algèbres de Lie associées aux schémas abéliens, Note C.R.A.S.t. 299 I n°5 (1984), 137-140. Zbl0609.14024MR756310
  2. [A2] André, Y., Quatre descriptions des groupes de Galois différentiels, Proceedings of the 'Séminaire d'algèbre de Paris', Springer, L.N. 1296. Zbl0651.12015
  3. [B] Borovoi, M., The Hodge group and the algebra of endomorphisms of an abelian variety; Questions of group theory and homological algebra (A.L. Onishchik, ed.), Yaroslav, Ges. Univ. 1981 (Russian). Zbl0494.14017MR709629
  4. [CKS] Cattani, E., Kaplan, A., Schmid, W., Degeneration of Hodge structure, Ann. Math.123 (1986) 457-535. Zbl0617.14005MR840721
  5. [CG] Cornalba, M., Griffiths, P., Some transcendental aspects of algebraic geometry, Proc. Symp. Pure Math. Vol. XXIX, AMS 1975, 3-110. Zbl0309.14007MR419438
  6. [D1] Deligne, P., Equations différentielles à points singuliers réguliers. LN 163 (1970) Springer. Zbl0244.14004MR417174
  7. [D2] Deligne, P., Théorie de Hodge. II. Publ. Math. IHES40 (1972), 5-57; III, Publ. Math. IHES44 (1974) 5-78. Zbl0219.14007MR498551
  8. [D3] Deligne, P., La conjecture de Weil pour les surfaces K3, Inv. Math.15 (1972), 206-226. Zbl0219.14022MR296076
  9. [DM] Deligne, P. and al., Hodge cycles, motives and Shimura varieties, Springer L.N. 900 (1982). I. Hodge cycles on abelian varieties 9-100. II. Tannakian categories 101-228. Zbl0477.14004MR654325
  10. [HZ] Hain, R.M., Zucker, S., Unipotent variations of mixed Hodge structure, Inv. Math.88 (1987), 83-124. Zbl0622.14007MR877008
  11. [K] Kashiwara, M., A study of variation of mixed Hodge structure, Publ. RIMS Kyoto Univ.22 (1986) 991-1024. Zbl0621.14007MR866665
  12. [Kz] Katz, N., Algebraic solutions of differential equations, Inv. Math.18 (1972), 1-118. Zbl0278.14004MR337959
  13. [M] Manin, Y., Rational points of algebraic curves over function fields, AMS transl. (2) 37, 59-78. Zbl0151.27601
  14. [Md] Mumford, D., Abelian Varieties, Oxford University Press, Oxford (1970). Zbl0223.14022MR282985
  15. [My] Murty, V.K., Exceptional Hodge classes on certain abelian varieties, Math. Ann.268 (1984), 197-205. Zbl0521.14004MR744607
  16. [Sd] Schmid, W., The singularities of the period mapping, Inv. Math.22 (1973), 211-319. Zbl0278.14003MR382272
  17. [S] Shimura, G., On analytic families of polarized abelian varieties and automorphic functions, Ann. of Math.78 (1963), 149-192. Zbl0142.05402MR156001
  18. [SZ] Steenbrink, J., Zucker, S., Variation of mixed Hodge structure. I. Inv. Math.80 (1985), 489-542. Zbl0626.14007MR791673
  19. [W] Waterhouse, W., Introduction to affine group schemes, Springer, Heidelberg, 1979. Zbl0442.14017MR547117

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