Ranks of Selmer Groups in an Analytic Family

  title={Ranks of Selmer Groups in an Analytic Family},
  author={Jo¨el Bella¨iche},
  • Jo¨el Bella¨iche
  • Published 2009
We study the variation of the dimension of the Bloch-Kato Selmer group of a p-adic Galois representation of a number field that varies in a refined family. We show that, if one restricts ourselves to representations that are, at every place dividing p, crystalline, non-critically refined, and with a fixed number of non-negative Hodge-Tate weights, then the dimension of the Selmer group varies essentially lower-semi-continuously. This allows to prove lower bounds for Selmer groups " by… CONTINUE READING

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