Abstract
In this paper we study absolutely irreducible integral λ-adic representations of the Galois groups of number fields. We assume that the representation satisfy the “Weil-Riemann conjecture” with weight n and prove that their dimension is bounded above by a constant, depending only on n and the rank of the corresponding λ-adic Lie algebras. As an application we obtain that the dimension of an Abelian variety is bounded above by the rank of its endomorphism ring times a certain constant, depending only on the semisimple rank of the corresponding ℓ-adic Lie algebra.
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Zarhin, Y.G. (1991). Finiteness theorems for dimensions of irreducible λ-adic representations. In: van der Geer, G., Oort, F., Steenbrink, J. (eds) Arithmetic Algebraic Geometry. Progress in Mathematics, vol 89. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0457-2_20
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DOI: https://doi.org/10.1007/978-1-4612-0457-2_20
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6769-0
Online ISBN: 978-1-4612-0457-2
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