On topological cyclic homology
T Nikolaus, P Scholze - 2018 - projecteuclid.org
Topological cyclic homology is a refinement of Connes–Tsygan's cyclic homology which
was introduced by Bökstedt–Hsiang–Madsen in 1993 as an approximation to algebraic K …
was introduced by Bökstedt–Hsiang–Madsen in 1993 as an approximation to algebraic K …
Some recent advances in topological Hochschild homology
A Mathew - Bulletin of the London Mathematical Society, 2022 - Wiley Online Library
Some recent advances in topological Hochschild homology - Mathew - 2022 - Bulletin of the
London Mathematical Society - Wiley Online Library Skip to Article Content Skip to Article …
London Mathematical Society - Wiley Online Library Skip to Article Content Skip to Article …
Differential cohomology in a cohesive infinity-topos
U Schreiber - arXiv preprint arXiv:1310.7930, 2013 - arxiv.org
We formulate differential cohomology and Chern-Weil theory--the theory of connections on
fiber bundles and of gauge fields--abstractly in the context of a certain class of higher …
fiber bundles and of gauge fields--abstractly in the context of a certain class of higher …
[HTML][HTML] K-theory and the bridge from motives to noncommutative motives
M Robalo - Advances in Mathematics, 2015 - Elsevier
In this work we present a new approach to the theory of noncommutative motives and use it
to explain the different flavors of algebraic K-theory of schemes and dg-categories. The work …
to explain the different flavors of algebraic K-theory of schemes and dg-categories. The work …
Universality of multiplicative infinite loop space machines
D Gepner, M Groth, T Nikolaus - Algebraic & Geometric Topology, 2016 - msp.org
We establish a canonical and unique tensor product for commutative monoids and groups in
an∞–category C which generalizes the ordinary tensor product of abelian groups. Using …
an∞–category C which generalizes the ordinary tensor product of abelian groups. Using …
Integrating quantum groups over surfaces
We apply the mechanism of factorization homology to construct and compute category‐
valued two‐dimensional topological field theories associated to braided tensor categories …
valued two‐dimensional topological field theories associated to braided tensor categories …
Hyperdescent and étale K-theory
D Clausen, A Mathew - Inventiones mathematicae, 2021 - Springer
We study the étale sheafification of algebraic K-theory, called étale K-theory. Our main
results show that étale K-theory is very close to a noncommutative invariant called Selmer K …
results show that étale K-theory is very close to a noncommutative invariant called Selmer K …
[HTML][HTML] The Galois group of a stable homotopy theory
A Mathew - Advances in Mathematics, 2016 - Elsevier
To a “stable homotopy theory”(a presentable, symmetric monoidal stable∞-category), we
naturally associate a category of finite étale algebra objects and, using Grothendieck's …
naturally associate a category of finite étale algebra objects and, using Grothendieck's …
[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 …