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2 results

  • tt-geometry of Tate motives over algebraically closed fields

  • Part of
  • Martin Gallauer
  • Journal:
    Compositio Mathematica / Volume 155 / Issue 10 / October 2019
    Published online by Cambridge University Press:
    06 September 2019, pp. 1888-1923
    Print publication:
    October 2019
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  • We study Tate motives with integral coefficients through the lens of tensor triangular geometry. For some base fields, including $\overline{\mathbb{Q}}$ and $\overline{\mathbb{F}_{p}}$, we arrive at a complete description of the tensor triangular spectrum and a classification of the thick tensor ideals.

  • On finite dimensionality of mixed Tate motives

  • Shahram Biglari
  • Journal:
    Journal of K-Theory / Volume 4 / Issue 1 / August 2009
    Published online by Cambridge University Press:
    04 September 2008, pp. 145-161
    Print publication:
    August 2009

  • We prove a few results concerning the notion of finite dimensionality of mixed Tate motives in the sense of Kimura and O'Sullivan. It is shown that being oddly or evenly finite dimensional is equivalent to vanishing of certain cohomology groups defined by means of the Levine weight filtration. We then explain the relation to the Grothendieck group of the triangulated category D of mixed Tate motives. This naturally gives rise to a λ–ring structure on K0(D).