3 citations · 4 across the 8 of their papers we have counts for
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K-theoretic Poitou-Tate duality in higher dimensions: proper case
Oliver Braunling
We generalize Blumberg-Mandell's K-theoretic Poitou-Tate duality to arithmetic schemes of arbitrary dimension, smooth and proper over S-integers. As in our earlier papers on the su…
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…
-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…
The -structure of the index map
Oliver Braunling, Michael Groechenig, Jesse Wolfson
Let be a local field with residue field . The classifying space of comes canonically equipped with a map to the delooping of the -theory space of . Passing t…
K-theory of locally compact modules over rings of integers
Oliver Braunling
We generalize a recent result of Clausen: For a number field with integers O, we compute the K-theory of locally compact O-modules. For the rational integers this recovers Clausen'…