Counter-examples to a conjecture of Karpenko for spin groups

Consider the canonical morphism from the Chow ring of a smooth variety \(X\) to the associated graded ring of the topological filtration on the Grothendieck ring of \(X\). In general, this morphism is not injective. However, Nikita Karpenko conjectured that these two rings are isomorphic for a gener...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2023-04
Hauptverfasser: Baek, Sanghoon, Devyatov, Rostislav
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:Consider the canonical morphism from the Chow ring of a smooth variety \(X\) to the associated graded ring of the topological filtration on the Grothendieck ring of \(X\). In general, this morphism is not injective. However, Nikita Karpenko conjectured that these two rings are isomorphic for a generically twisted flag variety \(X\) of a semisimple group \(G\). The conjecture was first disproved by Nobuaki Yagita for \(G=\mathop{\mathrm{Spin}}(2n+1)\) with \(n=8, 9\). Later, another counter-example to the conjecture was given by Karpenko and the first author for \(n=10\). In this note, we provide an infinite family of counter-examples to Karpenko's conjecture for any \(2\)-power integer \(n\) greater than \(4\). This generalizes Yagita's counter-example and its modification due to Karpenko for \(n=8\).
ISSN:2331-8422