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For rigid spaces, you can find a reference in Theorem 5.2.1, part 1 of Conrad's Irreducible components of rigid spaces. The statement for Berkovich spaces can be found in Proposition 3.4.6 of Berkovic …

Here is an expansion on my comment. For a field $K$, let $X$ be a normal projective $K$-variety, let $\mathscr{L}$ be a big line bundle on $X$, and let $D$ be a nonzero effective Cartier divisor on $X …

Setup. Let $K$ be an algebraically closed field of characteristic zero, and let $A/K$ be a simple abelian variety of dimension $n$. Let $\{ x_1,x_2,\dots,x_{m^{2n}}\}$ denote the $m$-torsion points of …

Setup. Let $K$ be an algebraically closed field of characteistic zero, let $X/K$ be a smooth projective surface and let $Z \subset X$ be an integral curve which is nonsingular except for a finite set …

Setup. Let $X$ be a compact complex manifold. Let $\sum\limits \omega_{jk}d{z_j}\otimes d\overline{z}_k$ be a Hermitian metric on $X$ with associated positive $(1,1)$-form $\omega = \frac{i}{2}\sum \o …

The below Magma code determines the size of $J_C(\mathbb{F}_p)$ for various primes $p$, and finally compute the GCD of their orders, which gives you a bound on the size of $J_C(\mathbb{Q})$. For a dis …

Setup. Let $k$ be an algebraically closed field of characteristic zero, and let $G/k$ be a semi-abelian variety i.e., $G$ is a commutative algebraic group which is an extension of an abelian variety $ …

Roughly speaking, the Kodaira dimension is an invariant of a variety that corresponds to curvature. One can show that curves of genus $\geq 2$ have Kodaira dimension 1 using Riemann-Roch. In Corollary …

Setup. Let $p > 2$ be a prime, let $K$ be the completion of the maximal unramified extension of $\mathbb{Q}_p$, and fix an algebraic closure $\overline{K}$ of $K$. Let $A/K$ be an abelian variety of d …

P. Bruin and F. Najman have determined the exceptional quadratic points on $X_0(33)$. See Table 8 of https://arxiv.org/pdf/1406.0655.pdf