Questions tagged [p-adic-integration]
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6
questions
11
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Closed image of curves under $p$-adic logarithm, Coleman integrals and Bogomolov
Disclaimer: my knowledge of $p$-adic analysis/geometry is minimal.
Consider a smooth, complete curve $C$ of genus $g$ over $\mathbb{C}_{p}$, denote by $J$ its Jacobian and consider the embedding $C\...
4
votes
1
answer
147
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Partition of unity for analytic manifolds over non-Archimedean local fields
I am looking for a reference to the following fact which, I hope, is correct.
Let $X$ be a compact analytic manifold over a non-Archimedean local field. Let
$X=\cup_\alpha U_\alpha$ be a finite open ...
2
votes
0
answers
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Formulation of $p$-adic Haar measure decomposition
$\DeclareMathOperator\GL{GL}\DeclareMathOperator\vol{vol}\DeclareMathOperator\diag{diag}$Suppose:
$F$ is a non-archimedean local field,
$\mathcal{O} \subset F$ its ring of integers,
$\pi \in \mathcal{...
10
votes
0
answers
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Elementary aspects of The Fargues-Fontaine curve
To any pair $(E,F)$, where $E$ is a local field and $F$ is a perfectoid field, one can associate a curve $X^{\text{FF}}_{E,F}$, the so-called Fargues-Fontaine curve, which is unique up to Frobenius ...
1
vote
1
answer
163
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Non-Archimedean Lebesgue dominated convergence theorem
In this paper, the authors explain that the full generality of the Lebesgue dominated convergence theorem holds for functions on a compact zero-dimensional space $X$ taking values in a metrically ...
3
votes
1
answer
419
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Bernoulli distributions and $p$-adic measure on $K$
The $p$-adic field $\mathbb{Q}_p$ has topological basis of open sets of the form $a+p^N \mathbb{Z}_p$ for $0 \leq a \leq p^N-1$ and $N \in \mathbb{Z}$. These are indeed compact open sets. One can ...