Related papers: Incomplete Tambara functors

We define a faithful contravariant functor NCSpec from the category of rings to the category of ringed spaces, and show that if R is a commutative ring then NCSpec(R) may be viewed as a completion of Spec(R) in an appropriate sense. We then…

We study homotopy-coherent commutative multiplicative structures on equivariant spaces and spectra. We define N-infinity operads, equivariant generalizations of E-infinity operads. Algebras in equivariant spectra over an N-infinity operad…

We lift to equivariant algebra three closely related classical algebraic concepts: abelian group objects in augmented commutative algebras, derivations, and K\"ahler differentials. We define Mackey functor objects in the category of Tambara…

We build new algebraic structures, which we call genuine equivariant operads, which can be thought of as a hybrid between equivariant operads and coefficient systems. We then prove an Elmendorf-Piacenza type theorem stating that equivariant…

We define the notion of an $\mathcal{RO}(G)$-graded Tambara functor and prove that any $G$-spectrum with norm multiplication gives rise to such an $\mathcal{RO}(G)$-graded Tambara functor.

We give, for every finite group G, a combinatorial description of the ring of G-Witt vectors on a polynomial algebra over the integers. Using this description we show that the functor, which takes a ring with trivial action of G to its ring…

In equivariant algebra, Mackey functors replace abelian groups and incomplete Tambara functors replace commutative rings. In this context, we prove that equivariant Hochschild homology can sometimes be computed using Mackey functor-valued…

Structures where we have both a contravariant (pullback) and a covariant (pushforward) functoriality that satisfy base change can be encoded by functors out of ($\infty$-)categories of spans (or correspondences). In this paper we study the…

We construct a globalization of Ferrand's norm functor over rings which generalizes it to the setting of a finite locally free morphism of schemes $T\to S$ of constant rank. It sends quasi-coherent modules over $T$ to quasi-coherent modules…

We prove that the map on Balmer spectra induced by a fully faithful geometric functor is a quotient map whose fibers are connected. This is an analogue of the Zariski Connectedness Theorem in algebraic geometry and it can be applied to a…

Inspired by equivariant homotopy theory, equivariant algebra studies generalisations of G-Mackey functors that do not have all transfer maps (also known as induction maps), for G a finite group. These incomplete Mackey functors have…

The normalized cochain complex of a simplicial set N^*(Y) is endowed with the structure of an E_{infinity} algebra. More specifically, we prove in a previous article that N^*(Y) is an algebra over the Barratt-Eccles operad. According to M.…

Let $F$ be an affine flat group scheme over a commutative ring $R$, and $S$ an $F$-algebra (an $R$-algebra on which $F$ acts). We define an equivariant analogue $Q_F(S)$ of the total ring of fractions $Q(S)$ of $S$. It is the largest…

A functor on compact Hausdorf spaces is constructed as the sum of certain equivariant K-theory groups. It is shown that the functor takes values in lambda-rings and satisfies a Thom isomorphism. In the case that the space is a CW-complex…

This paper establishes a theoretical framework connecting neural network learning with abstract algebraic structures. We first present a minimal counterexample demonstrating that standard neural networks completely fail on compositional…

For $N_\infty$ operads $\mathcal O$ and $\mathcal O'$ such that there is an inclusion of the associated indexing systems, there is a forgetful functor from incomplete Tambara functors over $\mathcal O'$ to incomplete Tambara functors over…

For a perfectoid ring $R$, we compute the full $\mathrm{RO}(\mathbb T)$-graded ring $\mathrm{TF}_\bigstar(R;\mathbf Z_p)$. This extends and simplifies work of Gerhardt and Angeltveit-Gerhardt. In even degrees, we find an…

Suppose $G$ is a finite group. In this paper, we construct an equivalence between the $\infty$-category of algebras over an $N_{\infty}$-operad $\mathcal{O}$ associated to a $G$-indexing system $\mathcal{I}$ and the corresponding…

Given a commutative ring $R$, a $\pi_1$-$R$-equivalence is a continuous map of spaces inducing an isomorphism on fundamental groups and an $R$-homology equivalence between universal covers. When $R$ is an algebraically closed field, Raptis…

Given commutative, unital rings $A$ and $B$ with a ring homomorphism $A\to B$ making $B$ free of finite rank as an $A$-module, we can ask for a "trace" or "norm" homomorphism taking algebraic data over $B$ to algebraic data over $A$. In…