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arXiv · 1204.5271

Monodromy of Galois representations and equal-rank subalgebra equivalence

Chun Yin Hui
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Abstract

We study l-independence of monodromy groups G_l of any compatible system of l-adic representations (in the sense of Serre) of number field K assuming semisimplicity. We prove that the formal character of the derived group of the identity component of G_l is independent of l and the (complexified) Lie algebra g_l of G_l satisfies an equal-rank subalgebra equivalence for all l. This equivalence is equivalent to the l-independence of the number of A_n factors for all n belonging to {6,9,10,11,...} and the parity of A_4 factors in g_l.

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Chun Yin Hui. 2012-04-24. Monodromy of Galois representations and equal-rank subalgebra equivalence. https://arxiv.org/abs/1204.5271

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