Motivic construction of cohomological invariants

Semenov, Nikita (2016): Motivic construction of cohomological invariants. In: Commentarii Mathematici Helvetici, Bd. 91, Nr. 1: S. 163-202

Abstract

Let G be a group of type E8 over Q such that GR is a compact Lie group, let K be a field of characteristic 0, and q=⟨⟨−1,−1,−1,−1,−1⟩⟩ a 5-fold Pfister form. J.-P. Serre posed in a letter to M. Rost written on June 23, 1999 the following problem: Is it true that GK is split if and only if qK is hyperbolic? In the present article we construct a cohomological invariant of degree 5 for groups of type E8 with trivial Rost invariant over any field k of characteristic 0, and putting k=Q answer positively this question of Serre. Aside from that, we show that a variety which possesses a special correspondence of Rost is a norm variety.

• Dokumententyp: Zeitschriftenartikel
• Publikationsform: Publisher's Version
• Keywords: Linear algebraic groups; cohomological invariants; algebraic cycles; algebraic cobordism; motivic cohomology; motives
• Fakultät: Mathematik, Informatik und Statistik > Mathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• Allianz-/Nationallizenz: Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
• Sprache: Englisch