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Results tagged with arithmetic-geometry
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user 4140
Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.
10
votes
Accepted
Trivial Weil-Châtelet group
Weil-Chatelet groups are huge. A theorem of Shafarevich states that if $n \ge 2$ and if $E$ is an elliptic curve (or an abelian variety) over a number field $k$ then $H^1(G_k,E)$ has infinitely many e …
- 3,142
9
votes
0
answers
322
views
Frey-Mazur for abelian varieties
Let $K$ be a number field. The Frey-Mazur conjecture asserts the existence of a constant $N_K$ such that for all primes $p>N_K$, and all pairs of elliptic curves $E_1$, $E_2/K$, if $\overline{\rho}_{E …
- 3,142
1
vote
0
answers
100
views
Points on the intersection of an affine quadric and cubic over a finite field
Are there absolute constants $N$ and $B$ such that the following is true?
Let $p>B$ be a prime. Let $q(x_0,\dotsc,x_n)$ and $c(x_0,\dotsc,x_n)$ be homogeneous of degree $2$ and $3$ with coefficients …
- 3,142