Whitehead ’ S Lemmas and Galois Cohomology of Abelian Varieties

  title={Whitehead ’ S Lemmas and Galois Cohomology of Abelian Varieties},
  author={Michael Larsen and Ren{\'e} Schoof},
Whitehead’s lemmas for Lie algebra cohomology translate into vanishing theorems for H and H in Galois cohomology. Via inflation-restriction, the H vanishing theorem leads to a simple formula for H(K, T`), where T` is the `-adic Tate module of an abelian variety over a number field K. We apply this formula to the “support problem” for abelian varieties. Under a suitable semisimplicity hypothesis for the Tate modules, we can give a refined version of the theorem of [6]. 


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