Elementary equivalence versus Isomorphism

初等可解亏减变种是可解的

Elementary anabelian varieties are anabelian

本文研究初等可解亏减变种的基本群同构与变种同构之间的双射关系，并证明占优映射与稳定同调注入映射之间的双射，验证了Grothendieck对Faltings的猜想。

Cartier isomorphism and Hodge Theory in the non-commutative case

These are lecture notes from Clay Summer School in Goettingen, in 2006; the lectures were an attempt at an elementary introduction to math.KT/0611623.

用单一域公理刻画有限生成域

Characterizing finitely generated fields by a single field axiom

本文证明每个有限生成域都可由一个一阶语句在同构意义下唯一刻画，解决了强初等等价与同构问题，其中特征二情形依赖奇点消解。

$\mathbb{F}_p$-expressible subalgebras and orbits of $\mathbb{E}(r,\mathfrak{g})$

For $G$ a connected, reductive group over an algebraically closed field $k$ of large characteristic, we use the canonical Springer isomorphism between the nilpotent variety of $\mathfrak{g}:=\mathrm{Lie}(G)$ and the unipotent variety of $G$ to study the projective variety of elementary subalgebras of rank $r$, denoted $\mathbb{E}(r,\mathfrak{g})$. In the case that $G$ is defined over $\mathbb{F}_p$, we define the category of $\mathbb{F}_p$-expressible subalgebras of $\mathfrak{g}$, and prove that this category is isomorphic to Quillen's category of elementary abelian subgroups of the finite Ch…