vix.ing · top · new · best · stats · spec

Geometric Height on Flag Varieties in Positive Characteristic

2024/12/01 by Chen, Yue, Yuan, Haoyang
#11G50 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2412.10393

Abstract

Let k be an algebraically closed field of characteristic p≠ 0. Let G be a connected reductive group over k, P ⊆ G be a parabolic subgroup and λ: P \longrightarrow G be a strictly anti-dominant character. Let C be a projective smooth curve over k with function field K=k(C) and F be a principal G-bundle on C. Then F/P \longrightarrow C is a flag bundle and Lλ=F ×P kλ on F/P is a relatively ample line bundle. We compute the height filtration and successive minima of the height function hLλ: X(K) \longrightarrow ℝ over the flag variety X=(F/P)K.

Related