3 citations · 4 across the 6 of their papers we have counts for
17 papers
A non-commutative analogue of Clausen's view on the idèle class group
Oliver Braunling, Ruben Henrard, Adam-Christiaan van Roosmalen
Clausen predicted that Chevalley's idèle class group of a number field appears as the first -group of the category of locally compact -vector spaces. This has turned out…
Classes in Zakharevich K-groups constructed from Quillen K-theory
Oliver Braunling, Michael Groechenig
We show that the K-groups K_{n}(O) for O the integers or an order in a CM field and n>0 appear as direct summands of the homotopy groups of various localisations of Zakharevich's K…
The standard realizations for the K-theory of varieties
Oliver Braunling, Michael Groechenig, Anubhav Nanavaty
The Grothendieck ring of varieties has well-known realization maps to, say, mixed Hodge structures or compactly supported -adic cohomology. Zakharevich and\ Campbell have dev…
-theory of locally compact modules over orders
Oliver Braunling, Ruben Henrard, Adam-Christiaan van Roosmalen
We present a quick approach to computing the -theory of the category of locally compact modules over any order in a semisimple -algebra. We obtain the -theory by…
Quinn's formula and abelian 3-cocycles for quadratic forms
Oliver Braunling
In pointed braided fusion categories knowing the self-symmetry braiding of simples is theoretically enough to reconstruct the associator and braiding on the entire category (up to…
Braided categorical groups and strictifying associators
Oliver Braunling
A key invariant of a braided categorical group is its quadratic form, introduced by Joyal and Street. We show that the categorical group is braided equivalent to a simultaneously s…