scholarly journals Iterated monodromy groups of Chebyshev-like maps on $\mathbb{C}^n$

2021 ◽  
Author(s):  
Joshua P. Bowman
Keyword(s):  
Monodromy Groups ◽  
Iterated Monodromy Groups

scholarly journals Iterated monodromy groups of quadratic polynomials, I

2008 ◽  
pp. 309-336 ◽  
Author(s):  
Laurent Bartholdi ◽  
Volodymyr Nekrashevych
Keyword(s):  
Quadratic Polynomials ◽  
Monodromy Groups ◽  
Iterated Monodromy Groups

scholarly journals Exponential growth of some iterated monodromy groups

2018 ◽  
Vol 116 (6) ◽  
pp. 1489-1518
Author(s):  
Mikhail Hlushchanka ◽  
Daniel Meyer
Keyword(s):  
Exponential Growth ◽  
Monodromy Groups ◽  
Iterated Monodromy Groups

scholarly journals Independence of algebraic monodromy groups in compatible systems

2021 ◽  
Vol 27 (4) ◽  
Author(s):  
Federico Amadio Guidi
Keyword(s):  
Galois Representations ◽  
Global Function ◽  
Irreducible Decomposition ◽  
Global Function Fields ◽  
Normal Varieties ◽  
Independence Result ◽  
Monodromy Groups ◽  
Independence Results ◽  
Lisse Sheaves ◽  
General Method

AbstractIn this paper we develop a general method to prove independence of algebraic monodromy groups in compatible systems of representations, and we apply it to deduce independence results for compatible systems both in automorphic and in positive characteristic settings. In the abstract case, we prove an independence result for compatible systems of Lie-irreducible representations, from which we deduce an independence result for compatible systems admitting what we call a Lie-irreducible decomposition. In the case of geometric compatible systems of Galois representations arising from certain classes of automorphic forms, we prove the existence of a Lie-irreducible decomposition. From this we deduce an independence result. We conclude with the case of compatible systems of Galois representations over global function fields, for which we prove the existence of a Lie-irreducible decomposition, and we deduce an independence result. From this we also deduce an independence result for compatible systems of lisse sheaves on normal varieties over finite fields.

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