Rigid local systems and motives of type G2

Michael Dettweiler, Stefan Reiter, Nicholas M. Katz

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

Using the middle convolution functor MCχ introduced by N.Katz, we prove the existence of rigid local systems whose monodromy is dense in the simple algebraic group G2. We derive the existence of motives for motivated cycles which have a motivic Galois group of type G2. Granting Grothendiecks standard conjectures, the existence of motives with motivic Galois group of type G2 can be deduced, giving a partial answer to a question of Serre.

Original languageEnglish (US)
Pages (from-to)929-963
Number of pages35
JournalCompositio Mathematica
Volume146
Issue number4
DOIs
StatePublished - Jul 2010

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Keywords

  • local systems
  • middle convolution
  • motives

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