12 citations · 65 across the 25 of their papers we have counts for
36 papers
Structure theorems for the heart of LCA
Oliver Braunling, Fei Ren
Cohomology theories with values in LCA (locally compact abelian) groups suffer from the problem that the latter do not form an abelian category. However, the category LCA has a can…
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…
Local compactness as the K(1)-local dual of finite generation
Oliver Braunling
Suppose R is any localization of the ring of integers of a number field. We show that the K-theory of finitely generated R-modules, and the K-theory of locally compact R-modules, a…
Hilbert reciprocity using K-theory localization
Oliver Braunling
Usually the boundary map in K-theory localization only gives the tame symbol at . It sees the tamely ramified part of the Hilbert symbol, but no wild ramification. Gillet ha…
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…
On the relative K-group in the ETNC, Part III
Oliver Braunling
The previous papers in this series were restricted to regular orders. In particular, we could not handle integral group rings, one of the most interesting cases of the ETNC. We res…
An alternative construction of equivariant Tamagawa numbers
Oliver Braunling
We propose a new formulation of the equivariant Tamagawa number conjecture (ETNC) for non-commutative coefficients. We remove Picard groupoids, determinant functors, virtual object…
Volume of line bundles via valuation vectors (different from Okounkov bodies)
Oliver Braunling
Up to a factor 1/n!, the volume of a big line bundle agrees with the Euclidean volume of its Okounkov body. The latter is the convex hull of top rank valuation vectors of sections,…
On the relative K-group in the ETNC, Part II
Oliver Braunling
In a previous paper we showed, under some assumptions, that the relative K-group in the Burns-Flach formulation of the equivariant Tamagawa number conjecture (ETNC) is canonically…
Automorphisms of OT manifolds and ray class numbers
Oliver Braunling, Victor Vuletescu
We compute the automorphism group of OT manifolds of simple type. We show that the graded pieces under a natural filtration are related to a certain ray class group of the underlyi…
On the relative K-group in the ETNC
Oliver Braunling
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 th…
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…
On the automorphic side of the K-theoretic Artin symbol
Peter Arndt, Oliver Braunling
Clausen has constructed a homotopical enrichment of the Artin reciprocity symbol in class field theory. On the Galois side, Selmer K-homology replaces the abelianized Galois group,…
On the homology of Lie algebras like
Oliver Braunling
We revisit a recent paper of Fialowski and Iohara. They compute the homology of the Lie algebra for an associative unital algebra over a field of char…
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'…
On the normally ordered tensor product and duality for Tate objects
Oliver Braunling, Michael Groechenig, Aron Heleodoro +1
This paper generalizes the normally ordered tensor product from Tate vector spaces to Tate objects over arbitrary exact categories. We show how to lift bi-right exact monoidal stru…
Multiplicative zeta function and logarithmic point counting over finite fields
Oliver Braunling
The zeta function of a motive over a finite field is multiplicative with respect to the direct sum of motives. It has beautiful analytic properties, as were predicted by the Weil c…
Torsion homology growth beyond asymptotics
Oliver Braunling
We show that (under mild assumptions) the generating function of log homology torsion of a knot exterior has a meromorphic continuation to the entire complex plane. As corollaries,…
K-theory of semi-linear endomorphisms via the Riemann-Hilbert correspondence
Oliver Braunling
Grayson, developing ideas of Quillen, has made computations of the K-theory of "semi-linear endomorphisms". In the present text we develop a technique to compute these groups in th…