Rigid local systems and motives of type G2

• Verfasst von: Dettweiler, Michael [VerfasserIn]
• Verfasst von: Reiter, Stefan [VerfasserIn]
• Titel: Rigid local systems and motives of type G2
• Titelzusatz: with an appendix by Michale Dettweiler and Nicholas M. Katz
• Mitwirkende: Katz, Nicholas M. [MitwirkendeR]
• Verf.angabe: Michael Dettweiler and Stefan Reiter
• E-Jahr: 2010
• Jahr: 24 March 2010
• Umfang: 35 S.
• Illustrationen: Illustrationen
• Fussnoten: Gesehen am 31.01.2024
• Titel Quelle: Enthalten in: Compositio mathematica
• Ort Quelle: Cambridge : Cambridge Univ. Press, 1935
• Jahr Quelle: 2010
• Band/Heft Quelle: 146(2010), 4, Seite 929-963
• ISSN Quelle: 1570-5846
• DOI: doi:10.1112/S0010437X10004641
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: 14C25 (secondary)
• Sach-SW: 14F05 (primary)
• Sach-SW: local systems
• Sach-SW: middle convolution
• Sach-SW: motives
• K10plus-PPN: 187965671X

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 Grothendieck’s 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.