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5
votes
3answers
477 views

A question on non-archimedian Fourier transform

Let $M(n)$ be the vector space of $n\times n$ matrices over a local non-archimedian field $K$. Let $\mathcal S$ denote the space of locally constant compactly supported functions on $M(n)$. Similarly, ...
3
votes
1answer
135 views

is every point of a Berkovich space a Shilov point?

Let $k$ be an algebraically closed non-Archimedean valued field with the value group $\mathbb R$, and let $X$ be a variety over $k$. Is it true that for any point $x \in X^{an}$ of the Berkovich ...
2
votes
0answers
74 views

The target of a regular function in Non-archimedean analytic geometry

Let $(k,|\cdot|)$ be an algebraically closed field, complete wrt a (multiplicative) norm as in the framework of the Berkovich's analytic geometry. Given a commutative Banach $k$-algebra ...
2
votes
2answers
164 views

injective implies completion injective?

Background and definitions. Let $k$ denote a field complete with respect to a non-trivial non-archimedean norm. Let $R$ be the integers in $k$, and say $\pi\in R$ with $0<|\pi|<1$ ($\pi$ ...
2
votes
0answers
103 views

Projective tensor powers of Banach spaces over a normed field

Let $E$ be a Banach space over a complete normed field $\mathbb K$. Is it possible to classify all proper $E$ for which the projective seminorm $p_n$ defined on the $n$-th tensor power of $E$ is a ...
3
votes
1answer
187 views

Spherical completions and flatness

Let $k$ be a non-Archimedean field. Does there exist a spherical completion $K$ of $k$ such that for any $k$-Banach space $X$, the natural map $X \to X \widehat{\otimes}K$ is an isometric embedding? ...
14
votes
1answer
548 views

Why do rigid spaces have “not enough points”?

In Brian Conrad's notes here for the 2007 Arizona winter school, bottom of p18, he says that there is an affinoid rigid-analytic space and a sheaf of abelian groups on it equipped with a non-zero ...
1
vote
0answers
167 views

Asymptotics vs Puiseux series

Define asymptotic as a class of sequences {$ x_i$},$_{i\in\mathbb N}$ modulo equivalence {$x_i$}={$y_i$} if $\lim_{i\to\infty} (x_i/y_i)=c\in\mathbb R,c\ne 0$. More, we define $X= \{x_i\} \lt Y= \{ ...
11
votes
1answer
447 views

bornological vector spaces over a non-archimedean field

Let $k$ be a complete non-archimedean field. In definitions I have seen of bornological vector spaces over $k$ there are usually some extra assumptions on the non-archimedean field. For instance in ...
2
votes
2answers
328 views

Non-archimedean group over the reals

Hi there, I have a totally ordered group $(\mathbb{R};\leq,\oplus,0,-)$ with the reals as base set satisfying monotonicity, i.e. for all $x,y,z$ we have that if $y\leq z$ then $x\oplus y \leq x\oplus ...
0
votes
1answer
204 views

Non-Archimedean non-standard models for R

Let $\langle \mathbb{R}, 0, 1, +, \cdot, <\rangle$ be the standard model for $R$, and let $S$ be a countable model of $R$ (satisfying all true first-order statements in $R$). Is it true that the ...
8
votes
2answers
552 views

Does Rolle's Theorem imply Dedekind completeness?

I think the answer to the title question is "yes", but Gerald Edgar, in his comment on Does antidifferentiability of continuous functions imply Dedekind completeness? , points out an article (actually ...
9
votes
0answers
201 views

Does antidifferentiability of continuous functions imply Dedekind completeness?

Let $R$ be an ordered field, and let $I$ be {$x \in R: a < x < b$} for some $a < b$ in $R$. Define notions of $R$-continuity and $R$-differentiability for functions $f : I \rightarrow R$ by ...
3
votes
4answers
790 views

analysis over non-Archimedean ordered fields

Can anyone suggest any good references for (or any experts on) analysis over non-Archimedean ordered fields, such as the field of rational functions in one variable (ordered at 0, or if you prefer at ...