Feb 27, 2019
HARD Math Problem Solved In 1 Minute!
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HARD Math Problem Solved In 1 Minute!
A Problem WolframAlpha Can't Solve, But You Can (615 + x^2 = 2^y)
Video https://youtu.be/DOISjFviqkM
Blog post https://wp.me/p6aMk-88n
I wasn't entirely satisfied with my closing remarks in my last post; in particular I don't think I explained the term "functor of points" well in an arithmetic context. Luckily I just read somethin...
I wasn’t completely happy with my comments about the relation between the functor of points and rational points. Liu’s book came to the rescue and I discovered the correct way to look at “rational points” on schemes - as “sections” from the spectrum of a field. It’s a short post, so come have a read!
Schemes really are mysterious objects; in one form they manifest themselves as locally ringed spaces as we've defined them. But they also appear naturally as set-valued functors on the category of ...
NEW POST!
Here I introduce the “functor of points” approach to schemes. This seems ridiculously abstract (and indeed it involves jumping between quite a few different categories) but in some ways it feels like the “right” way to think about schemes. Essentially a scheme associated to a polynomial equation tells you what the variety associated to that polynomial looks like over every ring. The scheme itself can then be reconstructed from each of these varieties.
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