rigid analytic varieties, affinoid varieties, strictly convergent power series over non-archimedean fields

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13
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Are flat morphisms of analytic spaces open?

Let $f:X\to Y$ be a morphism of complex analytic spaces. Assume $f$ is flat (or, more generally, that there is a coherent sheaf on $X$ with support $X$ which is $f$-flat). Is $f$ an open map? The ...
26
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1answer
2k views

Structure on $X(k)$ for separated finite type alg. space $X$, for complete valued $k$.

Let $k$ be a field complete with respect to a non-archimedean absolute value, and $X$ a separated algebraic space of finite type over $k$. If $X$ is a scheme then $X(k)$ inherits a natural ...
8
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1answer
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Do Berkovich homogenous spaces exist?

Let G be a k-analytic group, and let H be a closed subgroup of G. Then does there exist a k-analytic space, which can be reasonably called the quotient G/H? Commentary: I realise that I am not being ...
2
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1answer
474 views

What are in units of an affinoid algebra?

Suppose that $K$ is a complete local field and $A$ is an affinoid $K$-algebra. Is there a known way to produce an explicit description of the units of $A$? Here is what I already know: write ...
9
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2answers
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Cohomology of rigid-analytic spaces

Let $R$ be a complete discrete valuation ring and let $K$ be its field of fractions. Suppose $X$ is a smooth rigid-anaytic space over $K$. Often it is convenient to have a model of $X$ whose ...
6
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3answers
443 views

Weierstrass points on rigid-analytic surfaces

Does a rigid-analytic surface defined over a nonarchimedean complete field have Weierstrass points (if its genus is big enough let's say)? Is there a good reference that (ideally) lists theorems for ...