# Tagged Questions

**1**

vote

**1**answer

159 views

### Is the number of twists of a curve with a section in a given field finite

Let $X$ be a smooth projective geometrically connected curve over a number field $k$ of genus $g\geq 2$.
Is the number of twists of $X$ always infinite? (The answer is no, because there aren't any ...

**0**

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**1**answer

203 views

### surjectivity of rational points induced by surjective map from affine space

Let $k$ be a local field of char $0$ (which is the case I concern).
Let $V$ be a variety defined over $k$ and
let $f: \mathbb A^n\to V$ be a surjective map
(over the algebraic closure of $k$) ...

**0**

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**1**answer

382 views

### Poitou-Tate dualities for Galois representations into power series rings?

Suppose $K$ is a finite extension of $\mathbf{Q}_p$, $A=K[[T_1,\dots,T_n]]$, $V$ a finite-rank free $A$-module, and $\rho:G_{\mathbf{Q}} \to \mathrm{GL}(V)$ a continuous Galois representation. Are ...

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**2**answers

751 views

### Compatibility of Bloch-Kato and Beilinson-Bloch

Suppose $V/K$ is a smooth projective variety. Let $\mathrm{Ch}^{j}(V)_{0}$
be the group of codimension-$j$ homologically trivial $K$-rational cycles on $V$, modulo rational equivalence. A conjecture ...