Corpus ID: 231933771

On curves in K-theory and TR

@inproceedings{McCandless2021OnCI,
  title={On curves in K-theory and TR},
  author={Jonas McCandless},
  year={2021}
}
We prove that TR is corepresentable by the reduced topological Hochschild homology of the flat affine line S[t] as a functor defined on the∞-category of cyclotomic spectra with values in the∞-category of spectra with Frobenius lifts, refining a result of Blumberg–Mandell. We define the notion of an integral topological Cartier module using Barwick’s formalism of spectral Mackey functors on orbital ∞-categories, extending the work of Antieau–Nikolaus in the p-typical setting. As an application… Expand

References

SHOWING 1-10 OF 77 REFERENCES
The cyclotomic trace and algebraic K-theory of spaces
The cyclotomic trace is a map from algebraic K-theory of a group ring to a certain topological refinement of cyclic homology. The target is naturally mapped to topological Hochschild homology, andExpand
The de Rham-Witt complex and p-adic vanishing cycles
We determine the structure modulo p of the de Rham-Witt complex of a smooth scheme X over a discrete valuation ring of mixed characteristic with log-poles along the special fiber Y and show that theExpand
The cyclotomic trace and curves on K-theory
We give a functorial description of the topological cyclic homology of a ring A in terms of the relative algebraic K-theory of the truncated polynomial rings An=A[x]/xn. This description involves theExpand
On the Beilinson fiber square
Using topological cyclic homology, we give a refinement of Beilinson's $p$-adic Goodwillie isomorphism between relative continuous $K$-theory and cyclic homology. As a result, we generalize resultsExpand
MODELS OF G-SPECTRA AS PRESHEAVES OF SPECTRA
Let G be a finite group. We give Quillen equivalent models for the category of G-spectra as categories of spectrally enriched functors from ex- plicitly described domain categories to nonequivariantExpand
Cartier modules and cyclotomic spectra
We construct and study a t-structure on p-typical cyclotomic spectra and explain how to recover crystalline cohomology of smooth schemes over perfect fields using this t-structure. Our main tool is aExpand
Higher Algebraic K-Theory of Schemes and of Derived Categories
In this paper we prove a localization theorem for the K-theory of commutative rings and of schemes, Theorem 7.4, relating the K-groups of a scheme, of an open subscheme, and of the category of thoseExpand
Topological cyclic homology via the norm
We describe a construction of the cyclotomic structure on topological Hochschild homology ($THH$) of a ring spectrum using the Hill-Hopkins-Ravenel multiplicative norm. Our analysis takes placeExpand
FACTORIZATION HOMOLOGY OF ENRICHED ∞-CATEGORIES
For an arbitrary symmetric monoidal∞-category V, we define the factorization homology of V-enriched∞-categories over (possibly stratified) 1-manifolds and study its basic properties. In the case thatExpand
Parametrized higher category theory and higher algebra: Expos\'e IV -- Stability with respect to an orbital $\infty$-category
In this paper we develop a theory of stability for $G$-categories (presheaf of categories on the orbit category of $G$), where $G$ is a finite group. We give a description of Mackey functors asExpand
...
1
2
3
4
5
...