Author

Tian-Le Liu

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Preprint Aug 2026

A Fan Algorithm for Chow-Witt Rings of Smooth Projective Toric Varieties

Let $R$ be a real closed field and let $X_\Sigma$ be a smooth projective split toric variety. For an explicitly chosen basis rigidification $\mathfrak r$ of its Picard grading, we prove that the pair $(\Sigma,\mathfrak r)$ determines the resulting total Chow--Witt ring and give a terminating finite algorithm for all gr...

Hao-Yang Liu, Tian-Le Liu, Guo-Rui Xu · 0 citations

Preprint Aug 2026

Torus-enriched Motivic Bruhat Complexes and Maximal Compact Groups

Bruhat decompositions give cellular models for split algebraic groups, flag varieties, and maximal compact groups, but motivic boundaries retain orientation and torus-translation data lost in the flag quotient. Over a perfect field of characteristic zero, let the group be connected, split, semisimple, and simply connec...

Hao-Yang Liu, Tian-Le Liu · 1 citation