Positivity of Heights of Semistable Varieties

p-adic height pairings on abelian varieties with semistable ordinary reduction

We prove that for abelian varieties with semistable ordinary reduction the p-adic Mazur-Tate height pairing is induced by the unit root splitting of the Hodge filtration on the first deRham cohomology.

On heights of motives with semistable reduction

We study heights of motives with integral coefficients over number fields introduced by Kato. It is a generalization of the Faltings height of an abelian variety and we establish generalizations of some properties of the Faltings height in our context as conjectured by Kato. This sheds some light on integral structures of motives.

具有半稳定约化的 Motive 同构类中高度的有限性

Finiteness of Heights in Isogeny Classes of Motives with Semistable Reduction

本文利用积分 $p$-adic Hodge 理论推广了阿贝尔簇的 Faltings 高度，并在假设 adelic Mumford-Tate 猜想下，证明了 motive 同构类中高度的有限性，扩展了 Kisin 和 Mocz 的相关结果。

Semistable models for modular curves and power operations for Morava E-theories of height 2

We construct an integral model for Lubin-Tate curves as moduli of finite subgroups of formal deformations over complete Noetherian local rings. They are p-adic completions of the modular curves X_0(p) at a mod-p supersingular point. Our model is semistable in the sense that the only singularities of its special fiber are normal crossings. Given this model, we obtain a uniform presentation for the Dyer-Lashof algebra of Morava E-theories at height 2 as local moduli of power operations in elliptic cohomology.

K-半稳定Fano簇高度的确界I，环面情形

Sharp bounds on the height of K-semistable Fano varieties I, the toric case

受Fujita结果启发，本文猜想整数射影空间在K-半稳定度量算术Fano簇中高度最大，并在n≤6时证明了环面Fano簇的该猜想，给出了Donaldson环面不变量与Odaka模高度的尖锐下界。

Positivity of GIT heights of zero-cycles and hyperplane arrangements

In 1996 as part of the development of arithmetic intersection theory and Arakelov theory, Zhang defined a "GIT height function" for semi-stable algebraic cycles in projective space. In the same work, Zhang conjectured that this height function was positive. We prove this conjecture for zero-cycles and hyperplane arrangements.