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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
7
votes
Accepted
Global applications of eigenvarieties
This is something I've told people privately for a while, and now have enough ingredients written up (jointly with Liang Xiao) to claim on the web somewhere: the validity of the parity conjecture is c …
12
votes
2
answers
1k
views
Tate uniformization of nonsplit semistable elliptic curves
Let $E/\mathbf{Q}_p$ be an elliptic curve having split multiplicative reduction. Then Tate uniformization gives a surjective homomorphism of $p$-adic analytic groups $G_m \to E$, with infinite cyclic …