相关论文: Witt Vectors, Polynomial Maps, and Real Topologica…

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 define twisted Hochschild homology for Green functors. This construction is the algebraic analogue of the relative topological Hochschild homology $THH_{C_n}(-)$, and it describes the $E_2$ term of the K\"unneth spectral sequence for…

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…

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 arxiv:1602.04254, we have defined polynomial Witt vectors functor from vector spaces over a perfect field $k$ of positive characteristic $p$ to abelian groups. In this paper, we use polynomial Witt vectors to construct a functorial…

We prove that Real topological Hochschild homology can be characterized as the norm from the cyclic group of order $2$ to the orthogonal group $O(2)$. From this perspective, we then prove a multiplicative double coset formula for the…

The classical Witt vectors are a ubiquitous object in algebra and number theory. They arise as a functorial construction that takes perfect fields k of prime characteristic p > 0 to p-adically complete discrete valuation rings of…

This is an introduction to the theory of Witt vectors. It includes a construction of the Witt rings, the Frobenius and Verschiebung endomorphisms, the canonical map from W to W^2 (its lambda-algebra structure), the relation to strict…

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…

We give a new construction of $p$-typical Witt vectors with coefficients in terms of ghost maps and show that this construction is isomorphic to the one defined in terms of formal power series from the authors' previous paper. We show that…

The ring of Witt vectors $\mathbb{W} R$ over a base ring $R$ is an important tool in algebraic number theory and lies at the foundations of modern $p$-adic Hodge theory. $\mathbb{W} R$ has the interesting property that it constructs a ring…

This is the first part of a 2 part survey on the functor of the big and p-adic Witt vectors.

We study the homological algebra in the category $\mathcal{P}_p$ of strict polynomial functors of degree $p$ over a field of positive characteristic $p$. We determine the decomposition matrix of our category and we calculate the Ext-groups…

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…

For a prime $p$ and a commutative ring $R$ with unity, let $W(R)$ denote the group of $p$-typical Witt vectors. The group $W(R)$ is endowed with a Verschiebung operator $V: W(R)\to W(R)$ and a Teichm\"{u}ller map $\langle \ \rangle:…

We survey and extend the theory of Tambara functors. These are algebraic structures similar to Mackey functors, but with multiplicative norm maps as well as additive transfer maps, and a rule governing their interaction that is most easily…

This paper interprets Hesselholt and Madsen's real topological Hochschild homology functor THR in terms of the multiplicative norm construction. We show that THR satisfies cofinality and Morita invariance, and that it is suitably…

We give a concrete description of the category of etale algebras over the ring of Witt vectors of a given finite length with entries in an arbitrary ring. We do this not only for the classical p-typical and big Witt vector functors but also…

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…

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…