Motivic Decomposition of Projective Pseudo-Homogeneous Varieties

Abstract

ABSTRACT. Let G be a semi-simple algebraic group over a perfect field k. A lot of progress has been made recently in computing the Chow motives of projective G-homogeneous varieties. When k has positive characteristic, a broader class of G-homogeneous varieties appear. These are varieties over which G acts transitively with possibly non-reduced isotropy subgroup. In this paper we study these varieties which we call projective pseudo-homogeneous varieties for G inner type over k and prove that their motives satisfy Rost nilpotence. We also find their motivic decompositions and relate them to the motives of corresponding homogeneous varieties.

Correction to: MOTIVIC DECOMPOSITION OF PROJECTIVE PSEUDO-HOMOGENEOUS VARIETIES

“…Although the statement of the lemma is correct, here we state a stronger version of the lemma and prove it using a result of P. Deligne [Del18]. This gives an easy proof of Corollary 6.3 in [Sri17] which we also comment on. The rest of the paper is unaffected.…”

“…It was pointed out by Pierre Deligne that the proof of Lemma 6.2 in [Sri17] is incorrect. Although the statement of the lemma is correct, here we state a stronger version of the lemma and prove it using a result of P. Deligne [Del18].…”

“…Lemma 1 (Stronger version of Lemma 6.2 in [Sri17]). There exist k-morphisms f : X → X and g : X → X.…”

Bott-Samelson-Demazure-Hansen Varieties for Projective Homogeneous Varieties with Nonreduced Stabilizers

“…About the name of G{P with P nonreduced: G{P has been originally called the varieties of unseparated flag (vufs) by Haboush, Lauritzen, and Wenzel, e.g. in [HL93], and the projective pseudohomogeneous spaces in [Sri17]. However, G{P is a separated scheme and the action of G on G{P is transitive.…”