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Results tagged with arithmetic-geometry
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user 56667
Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
5
votes
Accepted
Reference Request: Preservation of étale maps under rigid analytic GAGA
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 …
- 998
6
votes
0
answers
437
views
Brauer-Manin obstruction to surfaces of Kodaira dimension 1
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 …
- 998
5
votes
0
answers
318
views
Ramification behavior of field given by adjoining $p$-torsion point on formal group of abeli...
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 …
- 998
5
votes
Finding $Q(\sqrt{-2})$-rational points on $X_0(33)$
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
- 998