…maybe Milne on etale cohmology: http://www.jmilne.org/math/CourseNotes/LEC210.pdf If you find that incomprehensible, start with Dummit and Foote's Abstract Algebra (read it cover to cover), Neukirch's Algebraic Number Theory, Atiyah and Macdonald's Commutative Algebra, and Fulton and Harris's Representation Theory. If you indeed want to read all that, you may as well enroll in a Ph.D. program in math....
……规律（比如 Cox 的《Primes of the Form x^2 + ny^2》）。但同样不可否认的是，当你真在做数学研究时，这类书远不如像 Neukirch 的《Algebraic Number Theory》这种晦涩难懂的大部头管用。就我个人的经历来说（我承认这经验样本太小，不一定有普遍性），前者胜在“见解”（insight）深刻，而后者充斥着太多不必要的“信息”（information）。直到我卡在……
…patterns (exempli gratia, Cox's "Primes of the Form x^2 + ny^2"). But it is also true that, when you are doing mathematics, such a book is not nearly as helpful as an impenetrable tome like Neukirch's Algebraic Number Theory. From my own experience (which, I'll admit, is not much to extrapolate from), the former was great for its "insight" and the latter just had too much unnecessary "information". Until I got stuck in…
……或许可以看看 Milne 写的 etale cohmology（平展上同调）：http://www.jmilne.org/math/CourseNotes/LEC210.pdf 如果你觉得这玩意儿完全看不懂，那就先从 Dummit 和 Foote 的《Abstract Algebra》（从头到尾通读一遍）、Neukirch 的《Algebraic Number Theory》、Atiyah 和 Macdonald 的《Commutative Algebra》以及 Fulton 和 Harris 的《Representation Theory》开始吧。要是你真打算把这些全啃完，那不如直接去读个数学 Ph.D. 算了……
…maybe Milne on etale cohmology: http://www.jmilne.org/math/CourseNotes/LEC210.pdf If you find that incomprehensible, start with Dummit and Foote's Abstract Algebra (read it cover to cover), Neukirch's Algebraic Number Theory, Atiyah and Macdonald's Commutative Algebra, and Fulton and Harris's Representation Theory. If you indeed want to read all that, you may as well enroll in a Ph.D. program in math....
……规律（比如 Cox 的《Primes of the Form x^2 + ny^2》）。但同样不可否认的是，当你真在做数学研究时，这类书远不如像 Neukirch 的《Algebraic Number Theory》这种晦涩难懂的大部头管用。就我个人的经历来说（我承认这经验样本太小，不一定有普遍性），前者胜在“见解”（insight）深刻，而后者充斥着太多不必要的“信息”（information）。直到我卡在……
…patterns (exempli gratia, Cox's "Primes of the Form x^2 + ny^2"). But it is also true that, when you are doing mathematics, such a book is not nearly as helpful as an impenetrable tome like Neukirch's Algebraic Number Theory. From my own experience (which, I'll admit, is not much to extrapolate from), the former was great for its "insight" and the latter just had too much unnecessary "information". Until I got stuck in…