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# The p-adic upper half plane

@inproceedings{Dasgupta2007ThePU, title={The p-adic upper half plane}, author={Samit Dasgupta and Jeremy Teitelbaum}, year={2007} }

- Published 2007

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