2011/12/28 by Yoichi Mieda, Mieda, Yoichi
Mathematics · #11F70 #14G35 #22E50 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1112.6116
openalex publication_date 2011/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper, we give a purely geometric approach to the local Jacquet-Langlands correspondence for GL(n) over a p-adic field, under the assumption that the invariant of the division algebra is 1/n. We use the l-adic etale cohomology of the Drinfeld tower to construct the correspondence at the level of the Grothendieck groups with rational coefficients. Moreover, assuming that n is prime, we prove that this correspondence preserves irreducible representations. This gives a purely local proof of the local Jacquet-Langlands correspondence in this case. We need neither a global automorphic technique nor detailed classification of supercuspidal representations of GL(n).