30.07.2026

Vikram Nadig (Bielefeld)

14:00

An important class of arithmetic groups is given by orthogonal groups, i.e. groups of isometries of forms over a number ring. The stable (co)homology of these groups can be accessed through Grothendieck–Witt theory, whose tractability has greatly increased due to recent work of Calmes, Dotto, Harpaz, Hebestreit, Land, Moi, Nardin, Nikolaus, and Steimle. Together with calculations in Grothendieck–Witt theory, the knowledge of homological stability for orthogonal groups would determine their (co)homology in low degrees. For isometries of quadratic forms, homological stability is known for very general rings and has been extensively studied, going back to the 1980s. This is in sharp contrast to the case of isometries of symmetric bilinear forms, for which no homological stability result was known over rings in which 2 is not a unit. I will report on recent work establishing homological stability for isometries of symmetric bilinear forms over a class of principal ideal domains that includes all fields, the integers, the Gaussian integers, and the Eisenstein integers.

SR 3.069