The p-adic upper half plane

  title={The p-adic upper half plane},
  author={Samit Dasgupta and Jeremy Teitelbaum},
The p-adic upper half plane X is a rigid analytic variety over a p-adic field K, on which the group GL2(K) acts, that Mumford introduced (as a formal scheme) as part of his efforts to generalize Tate’s p-adic uniformization of elliptic curves to curves of higher genus. The Cp–valued points of X are just P(Cp)−P(K), with GL2(K) acting by linear fractional transformations. Mumford showed that the appropriate generalization of Tate’s elliptic curves – the “totally split” curves of higher genus… CONTINUE READING