scholarly journals On the fundamental group schemes of certain quotient varieties

2021 ◽  
Vol 73 (4) ◽  
Author(s):  
Indranil Biswas ◽  
Phùng Hô Hai ◽  
João Pedro Dos Santos
Keyword(s):  
Fundamental Group ◽  
Group Schemes ◽  
Quotient Varieties

scholarly journals Higgs bundles and fundamental group schemes

2019 ◽  
Vol 19 (3) ◽  
pp. 381-388
Author(s):  
Indranil Biswas ◽  
Ugo Bruzzo ◽  
Sudarshan Gurjar
Keyword(s):  
Fundamental Group ◽  
Vector Bundles ◽  
Projective Variety ◽  
Group Scheme ◽  
Smooth Projective Variety ◽  
Higgs Bundles ◽  
Chern Classes ◽  
Group Schemes ◽  
Tannakian Category

Abstract Relying on a notion of “numerical effectiveness” for Higgs bundles, we show that the category of “numerically flat” Higgs vector bundles on a smooth projective variety X is a Tannakian category. We introduce the associated group scheme, that we call the “Higgs fundamental group scheme of X,” and show that its properties are related to a conjecture about the vanishing of the Chern classes of numerically flat Higgs vector bundles.

scholarly journals Fundamental group schemes for stratified sheaves

2007 ◽  
Vol 317 (2) ◽  
pp. 691-713 ◽  
Author(s):  
João Pedro Pinto dos Santos
Keyword(s):  
Fundamental Group ◽  
Group Schemes

Filling words in fundamental groups of Riemann surfaces

2013 ◽  
Vol 50 (1) ◽  
pp. 31-50
Author(s):  
C. Zhang
Keyword(s):  
Riemann Surface ◽  
Fundamental Group ◽  
Riemann Surfaces ◽  
Fundamental Groups ◽  
Closed Geodesics ◽  
New Words

The purpose of this article is to utilize some exiting words in the fundamental group of a Riemann surface to acquire new words that are represented by filling closed geodesics.

Representations of the fundamental group and the torsor of deformations. Global aspects

2017 ◽  
Author(s):  
Ahmed Abbes ◽  
Michel Gros
Keyword(s):  
Fundamental Group ◽  
Koszul Complex ◽  
Finiteness Conditions ◽  
Inverse Systems ◽  
Logarithmic Geometry

This chapter continues the construction and study of the p-adic Simpson correspondence and presents the global aspects of the theory of representations of the fundamental group and the torsor of deformations. After fixing the notation and general conventions, the chapter develops preliminaries and then introduces the results and complements on the notion of locally irreducible schemes. It also fixes the logarithmic geometry setting of the constructions and considers a number of results on the Koszul complex. Finally, it develops the formalism of additive categories up to isogeny and describes the inverse systems of a Faltings ringed topos, with a particular focus on the notion of adic modules and the finiteness conditions adapted to this setting. The chapter rounds up the discussion with sections on Higgs–Tate algebras and Dolbeault modules.

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