Why do we invert the Lefschetz motive?

Discussion in 'Math Research' started by bblloch1979, Dec 12, 2008.

  1. bblloch1979

    bblloch1979 Guest

    I have been reading through the construction of pure motives, and came
    across a fairly basic question which I am - unfortunately - having
    some trouble answering. The thing is that every step in the
    construction seems to be fairly natural up until the point when you
    decide to invert the Lefschetz motive. Why is it that we want to be
    able to invert this motive? What constructions is it that we are
    suddenly able to carry out once we have this extra motive (inverse of
    the Lefschetz motive)?
    If anyone out there knows of some good motivations/constructions that
    explains/justifies this final step in the construction of pure motives
    I would be all ears.
     
    bblloch1979, Dec 12, 2008
    #1

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  2. bblloch1979

    google Guest

    You have to invert the Lefschetz motive in order for motives to have
    duals, i.e., for the tensor category of motives to be rigid. See
    Saavedra 1972, VI 4.1.3.5.
     
    google, Dec 14, 2008
    #2

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