I walked on the banks of the Tiktok cock dock and sat down under the shade of a towering tech startup to find a really really really kino place to cry.....
My friend, Jackson Kerouac sat beside me on a chain pole indeed cross-legged balancing his body weight carefully nestling its tip between his slender buttocks leaving his butthole virgin like a saint floating in the air, companion, we Neuralinked™ each others brains to think of the bleak bleary gloomy dreary blue gray sad weary dark depressing rheumy dead somber dull dingy dark thesaurus final Frisco peaks.
Look at the SUNFLOWER, he said. There was a bleak bleary gloomy dreary blue gray sad weary dark depressing rheumy dead somber dull dingy dark shadow against the sky, sitting dry decrepid (etc) .
And the teal blue sunflower poised against the sunset, double masked like an Amherst student, double vaxxed under the prudent, invisible hand, baffling the sweet sun and beckoning a booster five months forward.
That mask was no man's mask but well actually it was but,
all that suit of sanitization, those cracked petals of excessive soap, that blurry soiled plexiglass vision, that sickeningly safe cleanliness and lack-of-dirt–medical–modern–all that civilization spotting your crazy golden crown–
and those blear thoughts of death and death and cases and death and cases and cases and omg we're LITERALLY in a pandemic, in the not-home-pile of used latex and cloth, blackened sanny wipes, final Frisco vax passes, le FUCK TRUMP chalk markings, virtuous floor signs stationed six feet apart, the cunty scent of misty boring clorox (not the cute and funny smell of mitsuboshi colors).
Unholy battered old thing you were, my sunflower OOOOOOOOOOOOOOOOOOOOO my soul, I loved you.
A perfect beauty of a sunflower! A perfect excellent lovely nice wonderful good great amazing fantastic final Frisco charming pretty splendid awesome cool keyed blah blah sunflower existence! woke up alive (not ded) and excited reaching in the sunset shadow sunrise sundown morning daytime midday noon afternoon evening dawn dusk golden monthly breeze!
How many smart crows GTFO away from you innocent of your sterilization, while you cursed the heavens of the doctors and your flower soul?
Poor dead flower? when did you forget you were a flower? when did you look at your skin and decide you were an impotent hypochondriac new wokeoid? the ghost of a wokeoid? the specter and shade of a once powerful mad American liberal?
[skipping two crap verses by ginsberg]
So I grabbed up the thicc sunflower and stuck it at my side like a bodypillow,
and deliver my sermon to my Tweeter account, and Jackson's Tweeter account, and anyone who'll hit like then not act upon it,
–We're not our thin skinned win, we're not blue white imageless vectors, we're golden sunflowers inside, blessed by our own seed & naked accomplishment-bodies (wtf is an "accomplishment-body") growing into mad blue formal sunflowers in the sunset, spied on on by our own government and people under the shadow of the mad hospital CCTV camera smartphone startup bleak bleary gloomy dreary blue gray sad weary dark depressing rheumy dead somber dull dingy dark riverbank sunset shadow sunrise sundown morning daytime midday noon afternoon dawn dusk final Frisco squarey Tiktok evening standup podcast sitdown kino vision.

Berkeley, CURRENT YEAR


Annnnnnnnnnnnnnnnd welcome to section 6! A day before the new month. What shall September bring us? O, what shall September bring? WHO KNOWS. Realize risk and go forth in your naked accomplishment-body, reader!

Fug. This section has so much abstract algebra. AAAAA. HOW AM I GOING TO MAKE IT THROUGH THIS SECTION LOL. Well, let's give this first exercise a shot then.

A

I tried but I can't do it lol FUCK MEEEEEEEEEE :'(((((

B

HAD TO LOOK ONLINE SORRY AGAIN FOLKS LOL FUUUUUUCK ME :'(((((((((((((((((

So we know from part A that Y is isomorphic to an open set U in A¹, right? Well, remember that A¹ has the finite complement topology, so all its closed sets are finite, so we can describe each set by their corresponding maximal ideals, or equivalently by the polynomial in A(A¹) = k[x] formed by multiplying those maximal ideals together. Hence, U = A¹ - Z(f) for some polynomial f. Now, going based off this guy, I should take the following closed set in A²:

Z

= Z(f(x)y - 1)

(I'm using x,y as the coordinates for A² here)

The maps

π : Z	→ Y
(x,y)	x
ϕ : Y	→ Z
x	(x, 1∕f(x))

"clearly" (lol, exercise left to reader) give a homeomorphism, so I know that Z is irreducible and thus a variety, and the π and ϕ furthermore make up an isomorphism. Done.

C

Attempt 1 was to show that R = k[x,y]∕(f(x)y - 1) is a UFD directly..... FAIL. Trying to show things directly has been failing on me quite often recently :(. Sooo, let's use TRICKY TRICKS!!!!! YAAYYYYYY TRICKY TRIX!1111!!!!! Okay, here's my idea: If an element has two distinct factorizations in R, then it should have two distinct factorizations in the local ring L = R_𝔪. Now by this ol' theorem:


I know that dim L = 1 (since Y is a curve here). Also, L is Noetherian and local... and a domain. So look at this theorem:


This tells us that L is a regular local ring, which is apparently a UFD. Which contradicts our assumption of distinct factors in L. Hence, R is a UFD. Done!

That proof was so abstract idk if it was even right LOL.