New York Journal of Mathematics
Volume 25 (2019), 1112-1177


Oliver Braunling

On the relative K-group in the ETNC

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Published: October 28, 2019.
Keywords: K-theory of exact categories, equivariant Tamagawa number conjecture, ETNC, locally compact modules.
Subject: Primary 19F99; Secondary 11R65 28C10.

We consider the Burns-Flach formulation of the equivariant Tamagawa number conjecture (ETNC). In their setup, a Tamagawa number is an element of a relative K-group. We show that this relative group agrees with an ordinary K-group, namely of the category of locally compact topological modules over the order. Its virtual objects are an equivariant Haar measure in a precise sense. We expect that all relative K-groups in the ETNC will have analogous interpretations. At present, we need to restrict to regular orders, e.g. hereditary.


The author was supported by DFG GK1821 "Cohomological Methods in Geometry" and a Junior Fellowship at the Freiburg Institute for Advanced Studies (FRIAS)

Author information

Oliver Braunling:
Freiburg Institute for Advanced Studies (FRIAS)
University of Freiburg
D-79104 Freiburg im Breisgau, Germany