English

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

Number Theory 2013-01-08 v2 Algebraic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.1108.5713,
  title  = {An alternative description of the Drinfeld p-adic half-plane},
  author = {Stephen Kudla and Michael Rapoport},
  journal= {arXiv preprint arXiv:1108.5713},
  year   = {2013}
}

Comments

18pp, Concluding remarks section revised. Typos corrected