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V. Golyshev: “Quantum Motives: Linearizations, Realizations, Use, Detections”

September 22, 2010, 11:07 am

Here are my notes from Golyshev’s talk in Bonn.

Golyshev_1_Bonn_Sep_2010

Summary:

  • a historical analogy: the study of Fano varieties now versus algebraic number theory prior to the proof of the Weil Conjectures
  • linearization and motives
  • Tannakian categories
  • the “quantum Tannakian category”
  • realizations in algebraic number theory: one can detect algebraic varieties by detecting their motives (in practice by detecting their L-functions via Selberg-Stark)
  • the “quantum Tate realization” and quantum detection
  • the Satake correspondence and its quantum parallel
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