After recalling the basic notions concerning profinite and proalgebraic group completions and Tannakian categories, we review how the latter can be used to define 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 define a Tannakian category whose objects are Higgs bundles on a complex projective variety that are ``numerically flat'' in a suitable sense, and show how the Higgs fundamental group is related to a conjecture about semistable Higgs bundles.

Tannakian categories, fundamental groups and Higgs bundles / Bruzzo, Ugo. - In: RENDICONTI DELL'ISTITUTO DI MATEMATICA DELL'UNIVERSITÀ DI TRIESTE. - ISSN 0049-4704. - 50(2018), pp. 149-159. [10.13137/2464-8728/22434]

Tannakian categories, fundamental groups and Higgs bundles

Bruzzo, Ugo
2018

Abstract

After recalling the basic notions concerning profinite and proalgebraic group completions and Tannakian categories, we review how the latter can be used to define 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 define a Tannakian category whose objects are Higgs bundles on a complex projective variety that are ``numerically flat'' in a suitable sense, and show how the Higgs fundamental group is related to a conjecture about semistable Higgs bundles.
RENDICONTI DELL'ISTITUTO DI MATEMATICA DELL'UNIVERSITÀ DI TRIESTE
50
149
159
Bruzzo, Ugo
File in questo prodotto:
File Dimensione Formato  
Bruzzo.pdf

accesso aperto

Tipologia: Versione Editoriale (PDF)
Licenza: Creative commons
Dimensione 223.45 kB
Formato Adobe PDF
223.45 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/85881
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? ND
social impact