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Abelian Varieties of K3 Type and ℓ-Adic Representations

  • Yuri G. Zarhin

Abstract

In this paper we study the algebraic envelopes of one-dimensional l-adic Lie algebras attached to the Galois actions on the Tate modules of Abelian varieties over finite fields. These envelopes are linear reductive commutative Lie algebras. We prove that these envelopes (after an extension of scalars) are generated by semisimple linear operators, whose spectrum coincides with the set of slopes of the Newton polygon of the Abelian variety. In addition, the multiplicity of each eigen value is equal to the length of the slope.

Keywords

Finite Field Galois Group Abelian Variety Newton Polygon Galois Action 
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Copyright information

© Springer-Verlag Tokyo 1991

Authors and Affiliations

  • Yuri G. Zarhin
    • 1
  1. 1.Research Computing Center of the USSR Academy of SciencesPushchino, Moscow RegionUSSR

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