Tensor product theorem for Hitchin pairs – An algebraic approach

Balaji, V.; Parameswaran, A.J.

Tensor product theorem for Hitchin pairs – An algebraic approach [ Théorème du produit tensoriel pour des paires de Hitchin – Une approche algébrique ]

Balaji, V. ; Parameswaran, A.J.

Annales de l'Institut Fourier, Tome 61 (2011) no. 6, p. 2361-2403

Résumé
Abstract

On donne une approche algébrique à l’étude des paires de Hitchin et on démontre le théorème du produit tensoriel pour des paires de Hitchin semistables sur les courbes projectives lisses définies sur un corps algébrique clos de caractéristique nulle ou bien de caractéristique

p

, où

p

désigne un nombre premier borné. On démontre aussi un théorème similaire pour des paires de Hitchin polystables.

We give an algebraic approach to the study of Hitchin pairs and prove the tensor product theorem for Higgs semistable Hitchin pairs over smooth projective curves defined over algebraically closed fields of characteristic zero and characteristic

p

, with

p

satisfying some natural bounds. We also prove the corresponding theorem for polystable Hitchin pairs.

MR 2976315 | Zbl 1248.14046

DOI : https://doi.org/10.5802/aif.2677
Classification: 14J60, 14D20
Mots clés: paires de Hitchin semistables, catégories Tannakiennes, schémas en groupes, produit tensoriel

@article{AIF_2011__61_6_2361_0,
     author = {Balaji, V. and Parameswaran, A.J.},
     title = {Tensor product theorem for Hitchin pairs -- An algebraic approach},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {61},
     number = {6},
     year = {2011},
     pages = {2361-2403},
     doi = {10.5802/aif.2677},
     mrnumber = {2976315},
     zbl = {1248.14046},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2011__61_6_2361_0}
}

Balaji, V.; Parameswaran, A.J. Tensor product theorem for Hitchin pairs – An algebraic approach. Annales de l'Institut Fourier, Tome 61 (2011) no. 6, pp. 2361-2403. doi : 10.5802/aif.2677. http://www.numdam.org/item/AIF_2011__61_6_2361_0/

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