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pro vyhledávání: '"19D55"'
Autor:
Read, Thomas
We study the homotopy groups of the geometric fixed points of the real topological cyclic homology of $\mathbb{Z}/4$. We relate these groups to the values of the non-abelian derived functors of the functor $M \mapsto (M \otimes_{\mathbb{Z}/4} M)^{C_2
Externí odkaz:
http://arxiv.org/abs/2411.11993
We study algebraic K-theory and topological Hochschild homology in the setting of bimodules over a stable category, a datum we refer to as a laced category. We show that in this setting both K-theory and THH carry universal properties, the former def
Externí odkaz:
http://arxiv.org/abs/2411.04743
Autor:
Meyer, Samuel, Wagner, Ferdinand
As a consequence of Efimov's proof of rigidity of the $\infty$-category of localising motives, Scholze and Efimov have constructed refinements of localising invariants such as $\operatorname{TC}^-$. In this article we compute the homotopy groups of t
Externí odkaz:
http://arxiv.org/abs/2410.23115
Autor:
Carmeli, Shachar, Luecke, Kiran
It is well known that the $[0,1]$ and $[0,2]$ Postnikov truncations of the units of the topological $K$-theories $\glone \KO$ and $\glone \KU$, respectively, are split, and that the splitting is provided by the ($\Z/2$-graded) line bundles. In this p
Externí odkaz:
http://arxiv.org/abs/2410.10126
We compute the MU-based syntomic cohomologies, mod $(p,v_1,\cdots,v_{n+1})$, of all $\mathbb{E}_1$-MU-algebra forms of connective Morava K-theory k(n). As qualitative consequences, we deduce the Lichtenbaum--Quillen conjecture, telescope conjecture,
Externí odkaz:
http://arxiv.org/abs/2410.07048
The topological Hochschild homology of a ring (or ring spectrum) $R$ is an $S^1$-spectrum, and the fixed points of THH($R$) for subgroups $C_n\subset S^1$ have been widely studied due to their use in algebraic K-theory computations. Hesselholt and Ma
Externí odkaz:
http://arxiv.org/abs/2409.05965
A conjecture due to Y. Han asks whether that Hochschild homology groups of a finite dimensional algebra vanish for sufficiently large degrees would imply that the algebra is of finite global dimension. We investigate this conjecture from the viewpoin
Externí odkaz:
http://arxiv.org/abs/2409.00945
Autor:
Lewis, Chloe
In this paper, we construct a Real equivariant version of the B\"okstedt spectral sequence which takes inputs in the theory of Real Hochschild homology developed by Angelini-Knoll, Gerhardt, and Hill and converges to the equivariant homology of Real
Externí odkaz:
http://arxiv.org/abs/2408.07188
Autor:
Brown, Michael K., Walker, Mark E.
Given a complex affine hypersurface with isolated singularity determined by a homogeneous polynomial, we identify the noncommutative Hodge structure on the periodic cyclic homology of its singularity category with the classical Hodge structure on the
Externí odkaz:
http://arxiv.org/abs/2407.09988
Autor:
Efimov, Alexander I.
In this paper we introduce and study the so-called continuous $K$-theory for a certain class of "large" stable $\infty$-categories, more precisely, for dualizable presentable categories. For compactly generated categories, the continuous $K$-theory i
Externí odkaz:
http://arxiv.org/abs/2405.12169