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36
votes
0answers
1k views

To what extent does Spec R determine Spec of the Witt vector ring over R?

Let $R$ be a perfect $\mathbb{F}_p$-algebra and write $W(R)$ for the Witt ring [i.e., ring of Witt vectors -- PLC] on $R$. I want to know how much we can deduce about $\text{Spec } W(R)$ from ...
6
votes
0answers
177 views

Power series defined by Witt vectors / Teichmüller representatives of p-adics

Let $K$ be $\mathbb{Q}_p$ for some prime $p$ (or more generally an unramified extension $W(\mathbb{F}_q)$ of $\mathbb{Q}_p$). If $\xi \in K$, we can write it in a unique way in the form $\sum a_i ...
6
votes
0answers
620 views

Ghost-Witt sequences vs. ghost-Polya-Burnside sequences?

If you're in a hurry scroll down until the questions: First the known part: A sequence $\left(b_1,b_2,b_3,...\right)$ of integers will be called a ghost-Witt sequence if there exists a sequence ...
3
votes
0answers
87 views

Efficiently computing (plethysm-like?)substitutions of symmetric functions

This is a rather technical question, it arose in connection of some calculations that I need to have better grasp of the question Formal group law over $\mathbb{F}_p$ and my own older one What is ...
2
votes
0answers
149 views

Ring of Witt Vectors and Tensor product of Fields

Let $p > 2$ be a prime, and let $\textbf{F}_{p} = \textbf{Z}/p\textbf{Z}$. Let $k_{1}$ be a finite field over $\textbf{F}_{p}$, and let $k$ be a perfect field of characteristic $p$. Then we have ...
1
vote
0answers
293 views

Has anyone used this theorem of P. Cartier?

In "Groupes Algebriques et Groupes Formels", Conf. au coll. sur la theorie des groupes algebriques, Bruxelles 1962, P. Cartier proves the following in Section 9, Theoreme 1: (What follows is my ...
-1
votes
0answers
77 views

Isomorphism of tensor product

The following question is related with the definition of the homothety operators defined in algebraic $K$-theory, more specific, in the Witt-vector module structure of the Bass Nil-groups of a ring ...