Uniformly effective boundedness of Shafarevich Conjecture-type

2013 ◽  
Vol 2013 (674) ◽  
Author(s):  
Gordon Heier
Keyword(s):  
Shafarevich Conjecture

scholarly journals Représentations linéaires des groupes kählériens : factorisations et conjecture de Shafarevich linéaire

2014 ◽  
Vol 151 (2) ◽  
pp. 351-376 ◽  
Author(s):  
Fréderic Campana ◽  
Benoît Claudon ◽  
Philippe Eyssidieux
Keyword(s):  
General Type ◽  
Linear Representation ◽  
Kähler Manifolds ◽  
Fundamental Groups ◽  
Kahler Manifolds ◽  
Shafarevich Conjecture ◽  
Classical Work ◽  
Projective Manifolds ◽  
Complex Projective ◽  
Holomorphic Convexity

AbstractWe extend to compact Kähler manifolds some classical results on linear representation of fundamental groups of complex projective manifolds. Our approach, based on an interversion lemma for fibrations with tori versus general type manifolds as fibers, gives a refinement of the classical work of Zuo. We extend to the Kähler case some general results on holomorphic convexity of coverings such as the linear Shafarevich conjecture.

On the Shafarevich conjecture for genus-2 fibrations

2008 ◽  
Vol 343 (4) ◽  
pp. 791-800 ◽  
Author(s):  
R. V. Gurjar ◽  
B. P. Purnaprajna
Keyword(s):  
Shafarevich Conjecture ◽  
Genus 2

scholarly journals The effective Shafarevich conjecture for abelian varieties of -type

2021 ◽  
Vol 9 ◽  
Author(s):  
Rafael von Känel
Keyword(s):  
Abelian Varieties ◽  
Integral Points ◽  
Arakelov Theory ◽  
Shafarevich Conjecture ◽  
Higher Dimensional ◽  
Hilbert Modular ◽  
Hilbert Modular Varieties ◽  
Modular Varieties ◽  
Formula Type ◽  
The Way

Abstract In this article we establish the effective Shafarevich conjecture for abelian varieties over ${\mathbb Q}$ of ${\text {GL}_2}$ -type. The proof combines Faltings’ method with Serre’s modularity conjecture, isogeny estimates and results from Arakelov theory. Our result opens the way for the effective study of integral points on certain higher dimensional moduli schemes such as, for example, Hilbert modular varieties.

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