Related papers: Noncommutative Symmetric Functions Associated with…

We use Lazard's universal $\pi$-ring to construct a variation of the $\pi$-typical ramified Witt vector functors, which we call the Lazardian Witt vector functor. We then use the Lazardian Witt vector functor to construct the universal…

Let K,S,D be a division ring, an endomorphism and a S-derivation of K, respectively. In this setting we introduce generalized noncommutative symmetric functions and obtain Vieta formula and decompositions of differential operators.…

The ring of Witt vectors associated to a ring R is a classical tool in algebra. We introduce a ring C(R) which is more easily constructed and which is isomorphic to the ring of Witt vectors W(R) for a perfect F_p-algebra R. It is obtained…

Using $\lambda$ operations, we give some results on the kernel of the natural map from the monoid algebra $\mathbb{Z} R$ of a commutative ring $R$ to the ring of $S$-Witt vectors of $R$. As a byproduct we obtain a very natural…

In this paper we develop a novel approach to Witt vector rings and to the (relative) de Rham Witt complex. We do this in the generality of arbitrary commutative algebras and arbitrary truncation sets. In our construction of Witt vector…

Following and generalizing a construction by Kontsevich, we associate a zeta function to any matrix with entries in a ring of noncommutative Laurent polynomials with integer coefficients. We show that such a zeta function is an algebraic…

For a prime $p$ and an associative ring $R$ with unity, there are various constructions of $p$-typical Witt vectors of $R$, all of which specialize to the classical $p$-typical Witt vectors when $R$ is commutative. These constructions are…

The purpose of this this paper is to generalize the functors arising from the theory of Witt vectors duto to Cartier. Given a polynomial $g(q)\in \mathbb Z[q]$, we construct a functor ${\overline {W}}^{g(q)}$ from the category of $\mathbb…

We extend the big and $p$-typical Witt vector functors from commutative rings to commutative semirings. In the case of the big Witt vectors, this is a repackaging of some standard facts about monomial and Schur positivity in the…

A very first step to develop non-commutative algebraic geometry is the arithmetic of polynomials in non-commuting variables over a commutative field, that is, the study of elements in free associative algebras. This investigation is…

We give a direct construction of the ring spectrum of spherical Witt vectors of a perfect $\mathbb{F}_p$-algebra R as the completion of the spherical monoid algebra $\mathbb{S}[R]$ of the multiplicative monoid $(R,\cdot)$ at the ideal $I =…

Motivated by a question of Rota, this paper studies the relationship between Rota--Baxter algebras and symmetric related functions. The starting point is the fact that the space of quasi-symmetric functions is spanned by monomial…

This article, which is substantially motivated by the previous joint work with J. McKay [8], establishes the analytic analogues of the relations we found free probability has with Witt vectors. Therefore, we first present a novel analytic…

We prove some results connecting the zeta functions of varieties over finite fields with the big Witt ring over $\mathbb Z$. We explore relations with motivic measures and a classical formula of Macdonald on invariants of symmetric products…

Global symmetries can be generalised to transformations generated by topological operators, including cases in which the topological operator does not have an inverse. A family of such topological operators are intimately related to…

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…

For every commutative ring $A$, one has a functorial commutative ring $W(A)$ of $p$-typical Witt vectors of $A$, an iterated extension of $A$ by itself. If $A$ is not commutative, it has been known since the pioneering work of L. Hesselholt…

We introduce the Hadamard topology on the Witt ring of rational functions, giving a simultaneous refinement of the weight and point-counting topologies. Zeta functions of algebraic varieties over finite fields are elements of the rational…

We describe a combinatorial approach to the analysis of the shape and orientation dependence of Wilson loop observables on two-dimensional noncommutative tori. Morita equivalence is used to map the computation of loop correlators onto the…

We give a new construction of the spherical Witt vector functor of Lurie and Burklund-Schlank-Yuan and extend it to nonconnective objects using synthetic spectra and recent work of Holeman. The spherical Witt vectors are used to build…