On Kummer extensions of the power series field

Local discriminants, kummerian extensions, and elliptic curves

Some thoughts on the congruence D=0,1(mod 4) for the absolute discriminant D of a number field

Division in modules and Kummer theory

In this work we generalize the concept of injective module and develop a theory of divisibility for modules over a general ring, which provides a general and unified framework to study Kummer-like field extensions arising from commutative algebraic groups. With these tools we provide an effective bound for the degree of the field extensions arising from division points of elliptic curves, extending previous results of Javan Peykar for CM curves and of Lombardo and the author for the non-CM case.

代数曲线的几何阿代尔上的 Kummer 理论

Kummer theory over the geometric adeles of an algebraic curve

本文利用几何阿代尔环的 Kummer 理论，通过证明 Picard 群平凡性、建立局部-全局原理及寻找分类不变量，对代数闭域上代数曲线的有限阿贝尔 Galois 覆叠进行了纯代数刻画。

The Loewy series of an FCP (distributive) ring extension

We examine the Loewy series associated to the lattice of subalgebras of an extension of commutative rings.

Green函子的平展扩张示例

Examples of étale extensions of Green functors

本研究将经典平展扩张示例迁移到等变语境，构造了Tambara函子类的Green函子平展扩张新示例，证明了$C_2$-Galois扩张、任意有限$n$的$C_n$-Kummer扩张及一般域平展扩张均可诱导对应Green函子的平展扩张。

Covers of the multiplicative group of an algebraically closed field of characteristic zero

We study the universal cover of the complex one-dimensional torus as a model-theoretic structure in a natural language. We consider also abstract covers of one-dimensional tori over algebraically closed fields of characteristic zero. The main result states that the structures can be described uniquely up to isomorphism by a simple (non-first order) sentence, given a fixed uncountable cardinality of the underlying field. The proof reduces to the Kummer theory of cyclic Galois extensions over some, not necessarily finitely generated fields.