All Questions
Tagged with p-adic-numbers p-adic
8 questions with no upvoted or accepted answers
3
votes
0
answers
118
views
Composition in function fields
Let $k=\mathbb F_q\left(\!\left(\frac1T\right)\!\right)$. One has the map: $\circ:k\times\{v\in k\mid\deg(v)>0\}\to k$ defined by $f\circ g=\sum_{n\ge-m}a_ng^{-n}$ where $f=\sum_{n\ge-m}a_n\frac1{T^...
- 3,998
2
votes
0
answers
75
views
Zeroes of the Euler series
Consider a prime $p$. Let $f$ be the Euler series defined by $f(z)=\sum_{n\ge0}n!z^n\}$. It is defined and analytic over $\mathcal D=\{z\in\mathbb C_p\mid v_p(z)>-\frac1{p-1}\}$. I try to check if ...
- 3,998
2
votes
0
answers
69
views
Invariant compact in division ring
Let $K$ be a discrete valued (with discrete valuation $v$) complete local division ring with ring of valuation $V$. Let $F$ be a compact subset of $V$. Suppose that for all $x\in F$ and for all $y\in ...
- 3,998
2
votes
0
answers
506
views
p-adic Lie theory
It is well known that exponential map in $C^{n\times n}$ will cover all non-sigular matrix $GL(n,C)$, which is a basic fact in Lie group and lie algebra theory, whether it is true for p-adic cases.
...
- 1,706
1
vote
0
answers
64
views
Continous morphisms of a local field with conditions in positive characteristic
Let $P$ be a an irreducible polynomial of $k:=\mathbb F_q(T)$, $\Omega_P$ be the completion of an algebraic closure $\overline{k_P}$ of $k_P$, the completion of $k$ for the topology induced by the $P$-...
- 3,998
1
vote
0
answers
201
views
Extension of $\mathbb C_p$?
Let $K/\mathbb Q$ be a finite algebraic extension. Consider a prime $p$ and $v$ be a valuation of $K$ above the valuation $v_p$ of $\mathbb Q_p$. Denote by $K_v$ a completion for the valuation $v$ of $...
- 3,998
0
votes
0
answers
139
views
continuous isomorphism of $p$-adic field
In Cassels-Frolich, one can read this theorem (page 57): Let $K$ be a finite finite separable extension of the valued field $(k,v)$. Let $\overline k$ be the completion of $k$ and $(K_j)_{1\le j\le r}$...
- 3,998
0
votes
0
answers
197
views
Name of some commutative ring akin to $p$-adics
I need help in identifying the naming convention of some commutative ring described below.
Let $p$ be a prime, let $k$ be a positive integer, and let $$\textbf{e} = (e_0,\ldots,e_{k-1})$$ be a list ...
- 103