这里是即将在 2024 ~ 2025 学年春季学期开设的代数几何讨论班讲义. 你可以在这个链接下载全部的讲义pdf, 也可以从我的博客进行浏览. 如果你发现了讲义中的错误, 欢迎在我的博客评论区对应章节指出, 我将不胜感激. ...
You can download following pdf from this link. ...
You can download following pdf from this link. ...
曾经在看一篇科普文章时得知了椭圆曲线的 Weierstrass 形式, 从那之后便对椭圆曲线产生了很强的兴趣. 如今终于学习了可以"与之一战"的数学工具---Riemann-Roch 定理. 本文将证明椭圆曲线都同构于形如 $Y^2T=X(X-T)(X-\lambda T)$ 的方程在 $P^2$ 中决定的曲线. ...
This document is a seminar note on singular homology. Before reading this article, make sure you have known the Chapter 1-3 of An Introduction to Algebraic Topology, written b…
Here is my note of the category theory, which is the basic of modern mathematics. While it's very useful, it's too hard and abstract to learn. I want to record my unde…
Sylow 定理是群论中的重要定理, 使我们更了解有限群的结构. 但是其证明过程在很多书上比较繁琐而且让人摸不着头脑, 本文整理了Advanced Modern Algebra 这本书中的证明方法, 其更为清晰且自然. ...
蛇形引理是同调代数中的一个重要引理, 在构造正合同调列中有起到重要的作用. ...
Definition 1.9.1 A domain $R$ is a unique factorization domain (UFD) or factorial ring if every $r\in R$, neither $0$ or a unit, is a product of irreducibles; if $p_1\cdots p_…
Definition 1.8.1 If $a,b$ lie in a commutative ring $R$, then a greatest common divisor (gcd) of $a,b$ is a common divisor $d\in R$ which is divisible by every common divisor;…