Related papers: Witt vectors with coefficients and TR

The ring of classic Witt vectors is a fundamental object in mixed characteristic commutative algebra which has many applications in number theory. There is a significant generalization due to Dress and Siebeneicher which for any profinite…

Let k be a perfect field of characteristic p and let $W_n(k)$ denote the p-typical Witt vectors of length n. For example, $W_n(\mathbb{F}_p)=\mathbb{Z}/p^n$. We study the algebraic K-theory of $W_n(k)$, and prove that $K(W_n(k))$ satisfies…

Over a perfect field $k$ of characteristic $p > 0$, we construct a ``Witt vector cohomology with compact supports'' for separated $k$-schemes of finite type, extending (after tensorisation with $\mathbb{Q}$) the classical theory for proper…

The rings of $p$-typical Witt vectors are interpreted as spaces of vanishing cycles for some perverse sheaves over a disc. This allows to "localize"\ an isomorphism emerging in Drinfeld's theory of prismatization [Dr], Prop. 3.5.1, namely…

The purpose of this article is to prove some results on the Witt vectors of perfect $\mathbf{F}_p$-algebras. Let $A$ be a perfect $\mathbf{F}_p$-algebra for a prime integer $p$ and assume that $A$ has the property $\mathbf{P}$. Then does…

We prove that the $p$-adically completed periodic topological cyclic homology of a DG category over a perfect field $k$ of characteristic $p>2$ is isomorphic to the ($p$-adically completed) periodic cyclic homology of a lifting of the DG…

For a not-necessarily commutative ring R we define an abelian group W(R;M) of Witt vectors with coefficients in an R-bimodule M. These groups generalize the usual big Witt vectors of commutative rings and we prove that they have analogous…

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 =…

We identify Whittaker vectors for $\mathcal{W}_k(\mathfrak{g})$-modules with partition functions of higher Airy structures. This implies that Gaiotto vectors, describing the fundamental class in the equivariant cohomology of a suitable…

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…

We introduce a new collection of partially global Galois cohomology classes subsuming both plectic Heegner points and mock plectic invariants. The former are recovered as localizations of plectic Heegner classes, while the latter arise as…

This work presents some results about Wick polynomials of a vector field renormalization in locally covariant algebraic quantum field theory in curved spacetime. General vector fields are pictured as sections of natural vector bundles over…

The ring of symmetric functions carries the structure of a Hopf algebra. When computing the coproduct of complete symmetric functions $h_\lambda$ one arrives at weighted sums over reverse plane partitions (RPP) involving binomial…

We describe the mod $p^r$ pro $K$-groups $\{K_n(A/I^s)/p^r\}_s$ of a regular local $\mathbb F_p$-algebra $A$ modulo powers of a suitable ideal $I$, in terms of logarithmic Hodge-Witt groups, by proving pro analogues of the theorems of…

This paper establishes a connection between equivariant ring spectra and Witt vectors in the sense of Dress and Siebeneicher. Given a commutative ringspectrum T in the highly structured sense, that is, an E-infinity-ringspectrum, with…

In a previous paper Cuntz and Deninger introduced the ring $C(R)$ for a perfect $\mathbb{F}_p$-algebra $R$. The ring $C(R)$ is canonically isomorphic to the $p$-typical Witt ring $W(R)$. In fact there exist canonical isomorphisms $\alpha_n…

Let A be a finitely generated algebra over a field K of characteristic p >0. We introduce a subring of the ring of Witt vectors W(A). We call it the ring of overconvergent Witt vectors. We prove that on a scheme X of finite type over K the…

This paper introduces and studies a class of Weyl-type algebras \(A_{p,t,\cA} = \Weyl{e^{\pm x^{p} e^{t x}},\; e^{\cA x},\; x^{\cA}}\) constructed over exponential-polynomial rings, where \(\FF\) is a field of characteristic zero, \(\cA\)…

The main purpose of this article is to give the integral cohomology of classical principal congruence subgroups in SL(2,Z) as well as their analogues in the third braid group with local coefficients in symmetric powers of the natural…

We show that functors like algebraic $K$-theory (such as unitary or symplectic $K$-functors), as well as the higher Grothendieck--Witt groups, possess the local constancy condition for Henselian valuation rings. Namely, taken with finite…