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40
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 ...
7
votes
0answers
213 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 ...
7
votes
0answers
628 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
50 views

Do any specializations of variables give valid equalities of series and products involving Witt symmetric functions?

Formally, Witt symmetric functions $w_n(x_1,x_2,...)$ ($n\geqslant1$) can be defined by $$ \prod_n(1-w_nt^n)=1+\sum_k(-1)^ke_kt^k=\prod_j(1-x_jt), $$ where $e_k(x_1,x_2,...)$ are the elementary ...
3
votes
0answers
118 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
97 views

Universal Witt vectors in full complete closed p-adic space omega?

Is there a p-adic mathematical structure that incorporates the advantages of both universal Witt vectors (not p-typical-limited; implementing Frobenius and Verschiebung operations) and permitting ...
2
votes
0answers
165 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
315 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 ...
0
votes
0answers
82 views

How is the p-adic norm calculated when using universal witt vectors?

How is the p-adic norm calculated when using UNIVERSAL WITT VECTORS? Is the p-adic norm calculated in the familiar way, in the sense that we look to the last digit to the right, and the prime number ...