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Title: | Tannakian categories, fundamental groups and Higgs bundles | Authors: | Bruzzo, Ugo | Keywords: | Fundamental groups; Tannakian categories; Higgs bundles; curve semistability | Issue Date: | 2018 | Publisher: | EUT Edizioni Università di Trieste | Source: | Ugo Bruzzo, "Tannakian categories, fundamental groups and Higgs bundles", in: "Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics vol. 50 (2018)", Trieste, EUT Edizioni Università di Trieste, 2018, pp. 149-159 | Abstract: | After recalling the basic notions concerning pro nite and proalgebraic group completions and Tannakian categories, we review how the latter can be used to de ne generalizations of the notion of fundamental group of a space, such as the Nori and Langer fundamental groups, and the algebraic fundamental group introduced by Simpson. Then we discuss how one can de ne a Tannakian category whose objects are Higgs bundles on a complex projective variety that are \numerically at" in a suitable sense, and show how the Higgs fundamental group is related to a conjecture about semistable Higgs bundles. |
Type: | Article | URI: | http://hdl.handle.net/10077/22434 | ISSN: | 0049-4704 | eISSN: | 2464-8728 | DOI: | 10.13137/2464-8728/22434 | Rights: | Attribution-NonCommercial-NoDerivatives 4.0 Internazionale |
Appears in Collections: | Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.50 (2018) |
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