A Weak Solution of Inverse Treblecross
We give a weak solution for an impartial game we called ``Inverse Treblecross''. We have determined which of its starting positions are $\mathscr{P}$-position and give a reasonable strategy.
math.CO↗
arXiv subjects
Muxi Li
Publications and source records attributed to Muxi Li.
Characterization of Beauville's algebraic numbers via Hodge theory
We provide a Hodge theoretical characterization of the set of algebraic numbers which arises from the complete list, due to A. Beauville, of semistable families of elliptic curves over $\mathbb{P}^1$ with four singular fibers. Our technical innovation is the analysis of the periodicity of the uniformizing Higgs bundle attached to $\mathbb{P}^1$ minus four points over the field of complex numbers.
math.AG↗
Integral Regulators for Higher Chow Complexes
Building on Kerr, Lewis and Mueller-Stach's work on the rational regulator, we prove the existence of an integral regulator on higher Chow complexes and give an explicit expression. This puts firm ground under some earlier results and speculations on the torsion in higher cycle groups by K-L-M, Petras, and Kerr-Yang.
math.AG↗
Two applications of the integral regulator
We review Li's refinement of the KLM regulator map, and use it to detect torsion phenomena in higher Chow groups.
math.AG↗
A Note on Linear Higher Chow Groups
We give a counterexample to the proof in the literature [K-Theory 25 (2002), 215-231] of the existence of linear representatives of higher Chow groups of number fields.
math.AG↗