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Karoubi’s relative Chern character and Beilinson’s regulator

Georg Tamme (2012)

Annales scientifiques de l'École Normale Supérieure

We construct a variant of Karoubi’s relative Chern character for smooth varieties over 𝐂 and prove a comparison result with Beilinson’s regulator with values in Deligne-Beilinson cohomology. As a corollary we obtain a new proof of Burgos’ Theorem that for number fields Borel’s regulator is twice Beilinson’s regulator.

Koszul duality and semisimplicity of Frobenius

Pramod N. Achar, Simon Riche (2013)

Annales de l’institut Fourier

A fundamental result of Beĭlinson–Ginzburg–Soergel states that on flag varieties and related spaces, a certain modified version of the category of -adic perverse sheaves exhibits a phenomenon known as Koszul duality. The modification essentially consists of discarding objects whose stalks carry a nonsemisimple action of Frobenius. In this paper, we prove that a number of common sheaf functors (various pull-backs and push-forwards) induce corresponding functors on the modified category or its triangulated...

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