# Tagged Questions

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

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### universal finite differential module of affinoid algebra

Let $k$ be a value field (archimedean), for example $k = \mathbb{Q}_p$, the p-adic field. The free Tate algebra is  T_n := \left\{ \ \sum a_I X^I, \ a_I \in k, \ a_I \rightarrow 0 \text{ as } |I| \...
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### Is the Gouvea-Mazur problem related to symmetric square $L$-functions?

Here's an idea that I've found appealing but have never been able to get anywhere with. One way to frame the Gouvea-Mazur question (for lack of a better term, since the original conjecture by the ...
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### Consequences of the geometric properties of the eigencurve

The eigencurve $\mathcal{E}$ is a rigid-analytic space parametrizing certain $p$-adic families of modular forms and associated Galois representations. By constructing an auxiliary reduced rigid curve ...
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### What is the nature of the zero locus of a section of a coherent sheaf?

Suppose that $X$ is a reduced rigid space and $\scr{F}$ is a coherent sheaf on $X$. For a section $f\in {\scr F}(X)$, the zero locus of $f$ is the set of points $x\in X$ at which $f$ vanishes in the ...
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### Tate models for semistable algebraic varieties with mixed reduction over a local field

It's known that if $A$ is an abelian variety of totally multiplicative reduction over a p-adic field K, then, after taking a finite field extension, it becomes isomorphic, as a rigid analytic group, ...