Local systems with tame, and a unipotent, local monodromy

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Flicker Y. Z., Özkan E.

Sao Paulo Journal of Mathematical Sciences, cilt.17, sa.2, ss.465-482, 2023 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1007/s40863-023-00374-8
  • Dergi Adı: Sao Paulo Journal of Mathematical Sciences
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.465-482
  • Anahtar Kelimeler: Automorphic representations, Counting, Curves over finite fields, Explicit trace formula, Local systems, Pseudo-coefficients, Tame and Steinberg representations, ℓ-adic representations
  • Marmara Üniversitesi Adresli: Hayır

Özet

We compute the cardinality of a set of Galois-invariant isomorphism classes of irreducible rank two Q¯ ℓ -smooth sheaves on X1- S1 , where X1 is a smooth projective absolutely irreducible curve of genus g over a finite field Fq and S1 is a reduced divisor, with pre-specified tamely ramified monodromy data at S, including precisely one point of principal unipotent monodromy, twisted by a tame character. Equivalently, we compute the number of the corresponding automorphic representations. The approach is based on using an explicit form of the trace formula for GL (2) , extending the work “Counting local systems with tame ramification” to include a Steinberg (= special) component, twisted by a tame character, by employing a pseudo-coefficient thereof.