# 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

- Mathematics
- 1993

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, and… Expand

The de Rham-Witt complex and p-adic vanishing cycles

- Mathematics
- 2003

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 the… Expand

The cyclotomic trace and curves on K-theory

- Mathematics
- 2005

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 the… Expand

On the Beilinson fiber square

- Mathematics
- 2020

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 results… Expand

MODELS OF G-SPECTRA AS PRESHEAVES OF SPECTRA

- Mathematics
- 2013

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 nonequivariant… Expand

Cartier modules and cyclotomic spectra

- Mathematics
- 2018

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 a… Expand

Higher Algebraic K-Theory of Schemes and of Derived Categories

- Mathematics
- 1990

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 those… Expand

Topological cyclic homology via the norm

- Mathematics
- 2014

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 place… Expand

FACTORIZATION HOMOLOGY OF ENRICHED ∞-CATEGORIES

- 2017

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 that… Expand

Parametrized higher category theory and higher algebra: Expos\'e IV -- Stability with respect to an orbital $\infty$-category

- Mathematics
- 2016

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 as… Expand