Simon Markett (Warwick):
Towards a motivic spectral sequence for hermitian K-theory
Zeit und Ort
Freitag, 24.4.15, 10:15-11:15, Raum 404, Eckerstr. 1
Zusammenfassung
The motivic spectral sequence can be seen as an analogue of the Atiyah-Hirzebruch spectral sequence in (complex) topological K-theory. Postulated by Quillen and Beilinson around 1980, it was finally shown to exist by a number of related results of Voevodsky, Grayson and Suslin in the 90s and early 2000s.\n\nBut the story doesn’t end here: For hermitian K-theory, often said to correspond to real topological K-theory, things are far from clear. In my talk I will present results from my dissertation that generalise Grayson’s ideas on this topic.\n\nI will begin with the basics and revise a certain construction of algebraic and hermitian K-theory. I will then explain conceptionally how spectral sequences can arise from a filtration of the K-theory space.\n\nFinally I will show how Grayson uses tuples of commuting elements of the general linear group to construct his tower and how their role is taken by orthogonal, symplectic, symmetric and antisymmetric matrices in the hermitian realm.