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7 votes
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intuition for lattices in p-adic (or other non-Archimedean) vector spaces?

I could use some help to jumpstart my intuition for lattices in vector spaces over non-Archimedean fields, like $\mathbb{Q}_p$ and $\mathbb{F}_q((t))$. I have some intuition for $\mathbb{Z}$-lattices ...
PrimeRibeyeDeal's user avatar
2 votes
0 answers
153 views

p-adic Banach space and complete tensor product

Let $p$ be a prime and $\mathbb{C}_{p}$ the completion of the algebraic closure of the $p$-adic number field $\mathbb{Q}_p$. Let $M$ be a $\mathbb{Q}_p$-Banach space. We denote by $M\mathbin{\widehat{\...
user521844's user avatar
0 votes
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88 views

Is There a $ p $-adic Analog of the Borsuk-Ulam Theorem?

The classical Borsuk-Ulam theorem states that any continuous map $ f: S^n \to \mathbb{R}^n $ from an $n $-dimensional sphere to $ n $-dimensional Euclidean space has a point $ x \in S^n $ such that $ ...
Kishalay Sarkar's user avatar
0 votes
0 answers
71 views

Space of non-archimedean characters is nonempty

Let $k$ be an algebraically closed complete non-archimedean field. Let $\mathcal{O}_k$ be its ring of integers. Suppose that $A$ is a $k$-Banach algebra, and $B$ is its closed unitary ball. Note that $...
Luiz Felipe Garcia's user avatar