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Could you describe what Grothendieck was doing in algerbiac geometry? Would studying the above get you up to the point of his work? If not, what are concrete su
by NiftyWalrus 8y ago
Could you describe what Grothendieck was doing in algerbiac geometry? Would studying the above get you up to the point of his work? If not, what are concrete suggestions that would get you there?
- obastani 8y agoThe "Background and history" section of the following article gives a very high-level idea of Grothendieck's contribution: https://en.wikipedia.org/wiki/Weil_conjectures https://en.wikipedia.org/wiki/Weil_conjectures
- NiftyWalrus 8y agoWhat is the modern path to study this area now? I’m sure it’s better understood now and one wouldn’t have to follow the historical approach to study the same concepts.
- obastani 8y agoI don't know myself, but here are some possible answers: https://mathoverflow.net/questions/114034/learning-path-for-the-proof-of-the-weil-conjectures https://mathoverflow.net/questions/114034/learning-path-for-... Edit: Here is another overview that seems good: https://www.math.ucdavis.edu/~osserman/math/pcm.pdf https://www.math.ucdavis.edu/~osserman/math/pcm.pdf
- MaysonL 8y agoTake a look at the stacks project: https://stacks.math.columbia.edu https://stacks.math.columbia.edu A cross between a wiki and a collaborative textbook.
- sdenton4 8y agoYeah, it's still incredibly difficult terrain, despite all the time that's passed. Wrestling with Hartsthorne is still a rite of passage for students in this area. I am (very) intrigued to know what would happen if someone made a serious effort to make the ideas more accessible. It remains an area where the depth of knowledge required is legitimately deep: would be cool to figure out which ideas are actually independent of other parts of the stack.