O. Braunling

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20112025

most citedTate Objects in Exact Categories (with appendix by Jan \vS\vtov\'ı\vcek and Jan Trlifaj)

12 citations · 65 across the 25 of their papers we have counts for

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15 papers · 1 filter

math.KT2025

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…

math.KT2023★ 1 cited

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…

math.KT2021

Hilbert reciprocity using K-theory localization

Oliver Braunling

Usually the boundary map in K-theory localization only gives the tame symbol at $K_{2}$ . It sees the tamely ramified part of the Hilbert symbol, but no wild ramification. Gillet ha…

math.KT2021

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 $F$ appears as the first $K$ -group of the category of locally compact $F$ -vector spaces. This has turned out…

math.KT2021

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…

math.KT2020

$K$ -theory of locally compact modules over orders

Oliver Braunling, Ruben Henrard, Adam-Christiaan van Roosmalen

We present a quick approach to computing the $K$ -theory of the category of locally compact modules over any order in a semisimple $Q$ -algebra. We obtain the $K$ -theory by…

math.KT2018

The $A_{\infty}$ -structure of the index map

Oliver Braunling, Michael Groechenig, Jesse Wolfson

Let $F$ be a local field with residue field $k$ . The classifying space of $G L_{n} (F)$ comes canonically equipped with a map to the delooping of the $K$ -theory space of $k$ . Passing t…

math.KT2017

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'…

math.KT2017

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…

math.KT2016

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…

math.KT2016★ 4 cited

Hochschild coniveau spectral sequence and the Beilinson residue

Oliver Braunling, Jesse Wolfson

We develop the Hochschild analogue of the coniveau spectral sequence and the Gersten complex. Since Hochschild homology does not have devissage or A^1-invariance, this is a little…

math.KT2015

Relative Tate Objects and Boundary Maps in the K-Theory of Coherent Sheaves

Oliver Braunling, Michael Groechenig, Jesse Wolfson

We investigate the properties of relative analogues of admissible Ind, Pro, and elementary Tate objects for pairs of exact categories, and give criteria for those categories to be…

math.KT2014★ 5 cited

The Index Map in Algebraic K-Theory

Oliver Braunling, Michael Groechenig, Jesse Wolfson

For a ring $R$ , we construct a universal $K_{R}$ -torsor $T_{R} \to K_{T a t e (R)}$ on the $K$ -theory space of Tate $R$ -modules. This torsor is closely related to canonical centra…

math.KT2014★ 12 cited

Tate Objects in Exact Categories (with appendix by Jan \vS\vtov\'ı\vcek and Jan Trlifaj)

Oliver Braunling, Michael Groechenig, Jesse Wolfson

We study elementary Tate objects in an exact category. We characterize the category of elementary Tate objects as the smallest sub-category of admissible Ind-Pro objects which cont…

math.KT2013★ 2 cited

Explicit Wodzicki excision in cyclic homology

O. Braunling

Assuming local one-sided units exist, I give an elementary proof of Wodzicki excision for cyclic homology. The proof is also constructive and provides an explicit inverse excision…

K-theoretic Poitou-Tate duality in higher dimensions: proper case

Local compactness as the K(1)-local dual of finite generation

Hilbert reciprocity using K-theory localization

A non-commutative analogue of Clausen's view on the idèle class group

Classes in Zakharevich K-groups constructed from Quillen K-theory

K-theory of locally compact modules over orders

The A∞​-structure of the index map

K-theory of locally compact modules over rings of integers

Multiplicative zeta function and logarithmic point counting over finite fields

K-theory of semi-linear endomorphisms via the Riemann-Hilbert correspondence

Hochschild coniveau spectral sequence and the Beilinson residue

Relative Tate Objects and Boundary Maps in the K-Theory of Coherent Sheaves

The Index Map in Algebraic K-Theory

Tate Objects in Exact Categories (with appendix by Jan \vS\vtov\'ı\vcek and Jan Trlifaj)

Explicit Wodzicki excision in cyclic homology

$K$ -theory of locally compact modules over orders

The $A_{\infty}$ -structure of the index map