Witt vectors and Tambara functors

循环群的 Burnside Tambara 函子的谱

The Spectrum of the Burnside Tambara Functor of a Cyclic Group

本文研究有限群 Burnside Tambara 函子的素理想谱，构造了一族素理想，并证明对循环群该族构成完整素谱，同时给出向更广泛群类推广的部分结果。

在等变代数中的根与幂零元

Radicals and Nilpotents in Equivariant Algebra

本文研究了等变代数中Tambara functor的根与幂零元，证明其nilradical由幂零元组成，并分类了导致T[1/x]=0的元素，同时指出这些元素在等变稳定茎中构成理想。

Witt Vectors, Polynomial Maps, and Real Topological Hochschild Homology

We show that various flavors of Witt vectors are functorial with respect to multiplicative polynomial laws of finite degree. We then deduce that the $p$-typical Witt vectors are functorial in multiplicative polynomial maps of degree at most $p-1$. This extra functoriality allows us to extend the $p$-typical Witt vectors functor from commutative rings to $\mathbb{Z}/2$-Tambara functors, for odd primes $p$. We use these Witt vectors for Tambara functors to describe the components of the dihedral fixed-points of the real topological Hochschild homology spectrum at odd primes.

等变代数中的代数闭域

Algebraically Closed Fields in Equivariant Algebra

本文借助 Burklund-Schlank-Yuan 的 Nullstellensatzian 抽象，刻画了有限群 G 上的 G-Tambara 函子，并证明其恰为代数闭域的余归纳，进而得到相应 K-理论谱的等价。

Lazardian Witt 向量

Lazardian Witt vectors

本文利用 Lazard 泛 π-环构造了 Lazardian Witt 向量函子，并借此构建 Lazardian 代数的泛剩余完美化。

Witt-Burnside functor attached to $\mathbf{Z}_p^2$ and $p$-adic Lipschitz continuous functions

Dress and Siebeneicher gave a significant generalization of the construction of Witt vectors, by producing for any profinite group $G$, a ring-valued functor $\mathbf{W}_G$. This paper gives a concrete interpretation of the rings $\mathbf{W}_{\mathbf{Z}_p^2}(k)$ where $k$ is a field of characteristic $p > 0$ in terms of rings of Lipschitz continuous functions on the $p$-adic upper half plane $\mathbf{P}^1(\mathbf{Q}_p)$. As a consequence we show that the Krull dimensions of the rings $\mathbf{W}_{\mathbf{Z}_p^d}(k)$ are infinite for $d \geq 2$ and we show the Teichmüller representatives form a…

A Witt-Burnside ring attached to a pro-dihedral group

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 group G produces a ring valued functor W_G, where the classic Witt vectors are recovered as the example G = Z_p. This article explores the structure of the image of this functor where G is the pro-2 group formed by taking the inverse limit of 2-power dihedral groups, and the image of W_G is taken on a field of characteristic 2.

On the structure of Witt-Burnside rings attached to pro-p groups

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 characteristic 0 with residue field k and are universal in that sense. A. Dress and C. Siebeneicher generalized this construction by producing a functor W_G attached to any profinite group G. The classical Witt vectors are those attached to the p-adic integers. Here we examine the ring structure of W_G(k) for several examples of pro-p groups G and fields k of characte…