Zobrazeno 1 - 10
of 105
pro vyhledávání: '"Braunling, Oliver"'
Autor:
Braunling, Oliver
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, are Anderson duals in the K(1)-local homotopy category. The same is tru
Externí odkaz:
http://arxiv.org/abs/2301.05943
Autor:
Braunling, Oliver
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 has shown how to prove Weil reciprocity using such boundary maps. This i
Externí odkaz:
http://arxiv.org/abs/2111.11580
Clausen predicted that Chevalley's id\`{e}le 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 to be true, and even generalizes to the higher $K$-groups in a sui
Externí odkaz:
http://arxiv.org/abs/2109.04331
Autor:
Braunling, Oliver, Groechenig, Michael
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 space. After rationalisation and going to the 1-connective cov
Externí odkaz:
http://arxiv.org/abs/2109.01136
The Grothendieck ring of varieties has well-known realization maps to, say, mixed Hodge structures or compactly supported $\ell$-adic cohomology. Zakharevich and\ Campbell have developed {a spectral refinement} of the Grothendieck ring of varieties.
Externí odkaz:
http://arxiv.org/abs/2107.01168
We present a quick approach to computing the $K$-theory of the category of locally compact modules over any order in a semisimple $\mathbb{Q}$-algebra. We obtain the $K$-theory by first quotienting out the compact modules and subsequently the vector
Externí odkaz:
http://arxiv.org/abs/2006.10878
Autor:
Braunling, Oliver
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 twisting by a braided monoidal auto-equivalence). We address the probl
Externí odkaz:
http://arxiv.org/abs/2005.05243
Autor:
Braunling, Oliver
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 skeletal and strictly associative one if and only if the polarization o
Externí odkaz:
http://arxiv.org/abs/1911.00130
Autor:
Braunling, Oliver
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 resolve this issue. We obtain versions of our main results valid for arbi
Externí odkaz:
http://arxiv.org/abs/1910.00448
Autor:
Braunling, Oliver
We propose a new formulation of the equivariant Tamagawa number conjecture (ETNC) for non-commutative coefficients. We remove Picard groupoids, determinant functors, virtual objects and relative K-groups. Our Tamagawa numbers lie in an idele group in
Externí odkaz:
http://arxiv.org/abs/1906.04686