Counting local systems with tame ramification

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We compute the cardinality of a set of Galois-invariant isomorphism classes of irreducible rank two Q¯-smooth sheaves on X-S, where X is a smooth projective absolutely irreducible curve of genus g over a finite field Fq and S is a reduced divisor, with pre-specified tamely ramified ramification data at S. Properties of this cardinality are studied. The approach is based on using a relatively elementary explicit form of the trace formula for GL(2), and introducing new types of almost pseudo-coefficients of principal series and discrete series representations.

Original languageEnglish
Pages (from-to)771-830
Number of pages60
JournalManuscripta Mathematica
Issue number3-4
StatePublished - Mar 2024


  • 11F70
  • 11F72
  • 11G20
  • 11R39
  • 11S37
  • 14H30
  • 22E35
  • 22E55


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