I am interested in learning what a scheme is if anyone wants to explain it to me.https://twitter.com/JadeMasterMath/status/1175126357774176256 …
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Replying to @JadeMasterMath
You want to construct a geometric object for each ring R so that R is the ring of 'good' functions into a field on that space. Evaluating the functions ought to give you a ring homomorphism onto the field, hence points correspond to quotients by maximal ideals.
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Replying to @SC_Griffith @JadeMasterMath
So you just take maximal ideals as points of the space. Now you need a topology. Level sets ought to be closed, and a vanishes at a point iff it's in the corresponding ideal, which tells you how to define the topology.
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Replying to @SC_Griffith @JadeMasterMath
Maps between the spaces ought to give you maps backwards between the associated rings, because you can pull functions back.
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Replying to @SC_Griffith @JadeMasterMath
The rest is probably best thought of as filling this stuff out with correct formalism (none of what I said is exactly)
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@SC_Griffith This is lovely. Thank you.
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