Specialization of monodromy group and l-independence

2011/10/21 by Hui, Chun Yin
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1110.4836

Abstract

Let E be an abelian scheme over a geometrically connected variety X defined over k, a finitely generated field over ℚ. Let η be the generic point of X and x∈ X a closed point. If \mathfrakg_l and (\mathfrakg_l)_x are the Lie algebras of the l-adic Galois representations for abelian varieties E_η and E_x, then (\mathfrakg_l)_x is embedded in \mathfrakg_l by specialization. We prove that the set \x∈ X closed point | (\mathfrakg_l)_x\subsetneq \mathfrakg_l\ is independent of l and confirm Conjecture 5.5 in [2].

Related

• Independence of l-adic representations of geometric Galois groups
• Monodromy of Galois representations and equal-rank subalgebra equivalence
• The abelian part of a compatible system and l-independence of the Tate conjecture
• Realizing Galois representations in abelian varieties by specialization
• Images of ℓ-adic representations and automorphisms of abelian varieties