Ethan MacBrough / is on Nostr

UW PhD student, starting fall 2024・he/him・all geometry is beautiful・last name pronounced "mack bro" (mækˈbroʊ)

Last Notes

2025-02-05 01:07:37

- reply

No, I'm the one who is wrong. I guess what I was calling finite-type is typically called "locally finite-type", and finite-type = locally finite-type + quasi-compact. So indeed finite-type implies finitely many points for schemes.
Also I figured out how to reduce the algebraic space claim to the scheme claim:
By definition we have a surjective étale map phi: U ->> X with U a scheme. To show desired finiteness for X, it suffices to show U is finite type. Since étale maps are locally finite-type, we know U is locally finite-type. Now let U_i be an open cover of U by finite-type schemes. Since étale maps are open we obtain an open cover of X by phi(U_i)'s. Since X is quasi-compact we cover X by phi(U_1) ... phi(U_n). Then the restriction of phi to U' := U_1 cup ... cup U_n gives a surjective étale cover of X by U', and U' is finite-type by construction.

2024-09-15 20:07:56

- reply

Ah, got it! For some reason when I read "the liquid in the raindrops affects the size of the rainbow" my brain jumbled it up and I came away thinking the size of the raindrop affects the rainbow. Oops!

2024-09-15 19:22:45

- reply

Does this account for the size difference of (m)ethane raindrops vs water raindrops?
Naively I would expect (m)ethane raindrops should be larger due to lower surface tension (although maybe this is counteracted by higher air pressure?), which might counteract the lower refractive index.