Explicit nonabelian LubinTate theory for GL(2)
Abstract
Let $F$ be a nonArchimedean local field with residue field $k$ of odd characteristic, and let $B/F$ be the division algebra of rank 4. We explicitly construct a stable curve $\mathfrak{X}$ over the algebraic closure of $k$ admitting an action of $GL_2(F)\times B^\times \times W_F$ which realizes the JacquetLanglands correspondence and the local Langlands correspondence in its cohomology.
 Publication:

arXiv eprints
 Pub Date:
 October 2009
 arXiv:
 arXiv:0910.1132
 Bibcode:
 2009arXiv0910.1132W
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Algebraic Geometry;
 11S37
 EPrint:
 33 pages, 3 figures. Comments highly welcomed