Title: The rank spectral sequence on Quillen's Q construction
Speaker: Bruno Kahn (Institut de Mathématiques de Jussieu-Paris Rive Gauche, Paris, France)
Date: 25 August 2022
Time: 12 pm
Venue: LH-1, Mathematics Department
I will explain a generalisation of the constructions Quillen used to prove that the $K$-groups
of rings of integers are finitely generated. It takes the form of a ‘rank’ spectral sequence,
converging to the homology of Quillen’s $Q$-construction on the category of coherent sheaves over
a Noetherian integral scheme, and whose $E^1$ terms are given by homology of Steinberg modules.
Computing its $d^1$ differentials is a challenge, which can be approached through the universal
modular symbols of Ash-Rudolph.