TY - JOUR
T1 - First covering of the drinfel’d upper half-plane and banach representations of GL2.(ℚp)
AU - Pan, Lue
N1 - Funding Information:
I heartily thank my advisor Richard Taylor for suggesting this problem and his constant encouragement and numerous discussions. I also wish to thank Gabriel Dospinescu, Yongquan Hu, and Ruochuan Liu for helpful discussions and for answering my questions. Finally, I would like to thank the referees for their careful work. The author was partially supported by NSF grant DMS-1252158.
Publisher Copyright:
© 2017 Mathematical Sciences Publishers.
PY - 2017
Y1 - 2017
N2 - For an odd prime p, we construct some admissible Banach representations of GL2.(ℚp) that conjecturally should correspond to some 2-dimensional tamely ramified, potentially Barsotti-Tate representations of Gal(ℚp/ℚp) via the p-adic local Langlands correspondence. To achieve this, we generalize Breuil’s work in the semistable case and work on the first covering of the Drinfel;d upper half-plane. Our main tool is an explicit semistable model of the first covering.
AB - For an odd prime p, we construct some admissible Banach representations of GL2.(ℚp) that conjecturally should correspond to some 2-dimensional tamely ramified, potentially Barsotti-Tate representations of Gal(ℚp/ℚp) via the p-adic local Langlands correspondence. To achieve this, we generalize Breuil’s work in the semistable case and work on the first covering of the Drinfel;d upper half-plane. Our main tool is an explicit semistable model of the first covering.
KW - Drinfel’d upper half-plane
KW - p-adic local Langlands correspondence of GL(ℚ)
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U2 - 10.2140/ant.2017.11.405
DO - 10.2140/ant.2017.11.405
M3 - Article
AN - SCOPUS:85018982354
SN - 1937-0652
VL - 11
SP - 405
EP - 503
JO - Algebra and Number Theory
JF - Algebra and Number Theory
IS - 2
ER -