Arithmetic Quotients of the Bruhat-Tits Building for Projective General Linear Groups in Positive Characteristic

Kondo S., Yasuda S.

MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.305, sa.1547, ss.1-110, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 305 Sayı: 1547
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1090/memo/1547
  • Dergi Adı: MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, MLA - Modern Language Association Database, zbMATH
  • Sayfa Sayıları: ss.1-110
  • Orta Doğu Teknik Üniversitesi Kuzey Kıbrıs Kampüsü Adresli: Evet

Özet

Let d >= 1. We study a subspace of the space of automorphic forms of GLd over a global field of positive characteristic (or, a function field of a curve over a finite field). We fix a place infinity of F , and we consider the subspace ASt consisting of automorphic forms such that the local component at infinity of the associated automorphic representation is the Steinberg representation (to be made precise in the text). We have two results. One theorem (Theorem 5.4.2) describes the constituents of ASt as automorphic representation and gives a multiplicity one type statement. For the other theorem (Theorem 4.5.1), we construct, using the geometry of the Bruhat-Tits building, an analogue of modular symbols in ASt integrally (that is, in the space of Z-valued automorphic forms). We show that the quotient is finite when a level is fixed and give a bound on the exponent of this quotient.