[PDF][PDF] Hermitian K-theory for stable∞-categories II: Cobordism categories and additivity
We define Grothendieck-Witt spectra in the setting of Poincaré-categories and show that
they fit into an extension with a K-and an L-theoretic part. As consequences, we deduce …
they fit into an extension with a K-and an L-theoretic part. As consequences, we deduce …
Stable moduli spaces of hermitian forms
F Hebestreit, W Steimle - arXiv preprint arXiv:2103.13911, 2021 - arxiv.org
We prove that Grothendieck-Witt spaces of Poincar\'e categories are, in many cases, group
completions of certain moduli spaces of hermitian forms. This, in particular, identifies …
completions of certain moduli spaces of hermitian forms. This, in particular, identifies …
HIGHER-THEORY OF FORMS I. FROM RINGS TO EXACT CATEGORIES
M Schlichting - Journal of the Institute of Mathematics of Jussieu, 2021 - cambridge.org
HIGHER K-THEORY OF FORMS I. FROM RINGS TO EXACT CATEGORIES Page 1 J. Inst.
Math. Jussieu (2021) 20(4), 1205–1273 doi:10.1017/S1474748019000410 c Cambridge …
Math. Jussieu (2021) 20(4), 1205–1273 doi:10.1017/S1474748019000410 c Cambridge …
Real topological Hochschild homology
This paper interprets Hesselholt and Madsen's real topological Hochschild homology functor
THR in terms of the multiplicative norm construction. We show that THR satisfies cofinality …
THR in terms of the multiplicative norm construction. We show that THR satisfies cofinality …
[HTML][HTML] Simplicial structures in higher Auslander–Reiten theory
We develop a novel combinatorial perspective on the higher Auslander algebras of type A, a
family of algebras arising in the context of Iyama's higher Auslander–Reiten theory. This …
family of algebras arising in the context of Iyama's higher Auslander–Reiten theory. This …
On the equivalence of two theories of real cyclotomic spectra
JD Quigley, J Shah - arXiv preprint arXiv:2112.07462, 2021 - arxiv.org
We give a new formula for real topological cyclic homology that refines the fiber sequence
formula discovered by Nikolaus and Scholze for topological cyclic homology to one …
formula discovered by Nikolaus and Scholze for topological cyclic homology to one …
On the parametrized Tate construction and two theories of real -cyclotomic spectra
JD Quigley, J Shah - arXiv preprint arXiv:1909.03920, 2019 - arxiv.org
We give a new formula for $ p $-typical real topological cyclic homology that refines the fiber
sequence formula discovered by Nikolaus and Scholze for $ p $-typical topological cyclic …
sequence formula discovered by Nikolaus and Scholze for $ p $-typical topological cyclic …
[HTML][HTML] A categorified Dold-Kan correspondence
T Dyckerhoff - Selecta Mathematica, 2021 - Springer
In this work, we establish a categorification of the classical Dold-Kan correspondence in the
form of an equivalence between suitably defined ∞∞-categories of simplicial stable ∞∞ …
form of an equivalence between suitably defined ∞∞-categories of simplicial stable ∞∞ …
On the parametrized Tate construction
JD Quigley, J Shah - arXiv preprint arXiv:2110.07707, 2021 - arxiv.org
We introduce and study a genuine equivariant refinement of the Tate construction
associated to an extension $\widehat {G} $ of a finite group $ G $ by a compact Lie group …
associated to an extension $\widehat {G} $ of a finite group $ G $ by a compact Lie group …
Higher Segal structures in algebraic -theory
T Poguntke - arXiv preprint arXiv:1709.06510, 2017 - arxiv.org
We introduce higher dimensional analogues of simplicial constructions due to Segal and
Waldhausen, respectively producing the direct sum and algebraic $ K $-theory spectra of an …
Waldhausen, respectively producing the direct sum and algebraic $ K $-theory spectra of an …