Local systems with tame, and a unipotent, local monodromy

Yuval Z. Flicker, Engin Özkan

Research output: Contribution to journalArticlepeer-review

Abstract

We compute the cardinality of a set of Galois-invariant isomorphism classes of irreducible rank two Q¯ -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.

Original languageEnglish
Pages (from-to)465-482
Number of pages18
JournalSao Paulo Journal of Mathematical Sciences
Volume17
Issue number2
DOIs
StatePublished - Dec 2023

Keywords

  • Automorphic representations
  • Counting
  • Curves over finite fields
  • Explicit trace formula
  • Local systems
  • Pseudo-coefficients
  • Tame and Steinberg representations
  • ℓ-adic representations

All Science Journal Classification (ASJC) codes

  • Statistics, Probability and Uncertainty
  • Computational Theory and Mathematics
  • General Mathematics

Fingerprint

Dive into the research topics of 'Local systems with tame, and a unipotent, local monodromy'. Together they form a unique fingerprint.

Cite this