Artin's criteria for algebraicity revisited

超曲线的超模群通过Artin准则的代数性

Algebraicity of supermoduli of curves via Artin's criteria

本文通过超几何的Artin代数性准则证明了四个超几何模群的代数性，包括超曲线、超黎曼面及其稳定形式，其中稳定超黎曼面的模群代数性有新证明，而稳定超曲线的模群代数性为新结果。

Artin--Hasse--Weil L-级数在整体函数域上的代数性

Algebraicity of Artin--Hasse--Weil L-series over global function fields

本文证明了整体函数域上阿贝尔簇的L-函数被Artin表示扭曲后的特殊值满足Deligne周期猜想的类比，并以椭圆曲线为例说明。

Artin's theorems in supergeometry

We generalize Artin's three main algebraicity theorems to the setting of supergeometry: Artin approximation, algebraization of formal moduli, and algebraization of stacks.

Openness of versality via coherent functors

We give a proof of openness of versality using coherent functors. As an application, we streamline Artin's criterion for algebraicity of a stack. We also introduce multi-step obstruction theories, employing them to produce obstruction theories for the stack of coherent sheaves, the Quot functor, and spaces of maps in the presence of non-flatness.

The Greenberg functor revisited

The proof, but not the statement, of Proposition 18.2 contained an error which is repaired in this version. See Remark 18.3 in this version. No other changes. We extend Greenberg's original construction to arbitrary (in particular, non-reduced) schemes over (certain types of) local artinian rings. We then establish a number of basic properties of the extended functor and determine, for example, its behavior under Weil restriction. We also discuss a formal analog of the functor.