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

Stephen Kudla[1]; Michael Rapoport[2]

  • [1] University of Toronto Department of Mathematics 40 St. George St., BA6290 Toronto, Ontario, M5S 2E4 (Canada)
  • [2] Mathematisches Institut der Universität Bonn Endenicher Allee 60 53115 Bonn (Allemagne)

Annales de l’institut Fourier (2014)

  • Volume: 64, Issue: 3, page 1203-1228
  • ISSN: 0373-0956

Abstract

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We show that the Deligne formal model of the Drinfeld p -adic half-plane relative to a local field F represents a moduli problem of polarized O F -modules with an action of the ring of integers 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 .

How to cite

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Kudla, Stephen, and Rapoport, Michael. "An alternative description of the Drinfeld $p$-adic half-plane." Annales de l’institut Fourier 64.3 (2014): 1203-1228. <http://eudml.org/doc/275434>.

@article{Kudla2014,
abstract = {We show that the Deligne formal model of the Drinfeld $p$-adic half-plane relative to a local field $F$ represents a moduli problem of polarized $O_F$-modules with an action of the ring of integers 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 $\{\rm SL\}_2(F)$ and $\{\rm SU\}(C)(F)$ for a two-dimensional split hermitian space $C$ for $E/F$.},
affiliation = {University of Toronto Department of Mathematics 40 St. George St., BA6290 Toronto, Ontario, M5S 2E4 (Canada); Mathematisches Institut der Universität Bonn Endenicher Allee 60 53115 Bonn (Allemagne)},
author = {Kudla, Stephen, Rapoport, Michael},
journal = {Annales de l’institut Fourier},
keywords = {Drinfeld $p$-adic half-plane; Bruhat-Tits tree; Drinfeld half plane; local fields; Drinfeld moduli problem},
language = {eng},
number = {3},
pages = {1203-1228},
publisher = {Association des Annales de l’institut Fourier},
title = {An alternative description of the Drinfeld $p$-adic half-plane},
url = {http://eudml.org/doc/275434},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Kudla, Stephen
AU - Rapoport, Michael
TI - An alternative description of the Drinfeld $p$-adic half-plane
JO - Annales de l’institut Fourier
PY - 2014
PB - Association des Annales de l’institut Fourier
VL - 64
IS - 3
SP - 1203
EP - 1228
AB - We show that the Deligne formal model of the Drinfeld $p$-adic half-plane relative to a local field $F$ represents a moduli problem of polarized $O_F$-modules with an action of the ring of integers 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 ${\rm SL}_2(F)$ and ${\rm SU}(C)(F)$ for a two-dimensional split hermitian space $C$ for $E/F$.
LA - eng
KW - Drinfeld $p$-adic half-plane; Bruhat-Tits tree; Drinfeld half plane; local fields; Drinfeld moduli problem
UR - http://eudml.org/doc/275434
ER -

References

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