Tensor product theorem for Hitchin pairs – An algebraic approach

Balaji, V.; Parameswaran, A.J.

doi:10.5802/aif.2677

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

Balaji, V.¹ ; Parameswaran, A.J.²

¹ Chennai Mathematical Institute SIPCOT IT Park Siruseri-603103 (India)
² Kerala School of Mathematics Kozhikode, Kerala and Tata Institute of Fundamental Research School of Mathematics Mumbai-400095 (India)

Annales de l'Institut Fourier, Tome 61 (2011) no. 6, pp. 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 Zbl

DOI : 10.5802/aif.2677

Classification : 14J60, 14D20
Keywords: Higgs semistable Hitchin pairs, Tannaka categories, group schemes, tensor products
Mot clés : paires de Hitchin semistables, catégories Tannakiennes, schémas en groupes, produit tensoriel

Affiliations des auteurs :

Balaji, V. ¹ ; Parameswaran, A.J. ²

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     title = {Tensor product theorem for {Hitchin} pairs {\textendash} {An} algebraic approach},
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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/articles/10.5802/aif.2677/

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