An alternative description of the Drinfeld p-adic half-plane

Details An alternative description of the Drinfeld p-adic half-plane An alternative description of the Drinfeld p-adic half-plane

2011-08-29

arxiv.org/abs/1108.5713v1

Mathematics

Number Theory

18pp

Scientific paper

We show that the Deligne formal model of the Drinfeld p-adic halfplane relative to a non-archimedean local field F represents a moduli problem of polarized O_F-modules with an action of the ring of integers O_E in a quadratic extension E of F. The proof proceeds by establishing a comparison isomorphism with the Drinfeld moduli problem. This isomorphism reflects the accidental isomorphism of SL_2(F) and SU(C)(F) for a two-dimensional split hermitian space C for E/F.

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