Posted by: holdenlee | September 10, 2012

Early fall

How does it feel to be leaf, clawing against the sidewalk with your tips, trying to grab a foothold against the stone-faced cement? The wind is like a baby, the only game he knows how to play with cards is turn the card over, laugh, then turn it over again, and toss it in a few different ways before he loses interest. It is nascent autumn, when all your friends are still green in their trees, and will go through all the vicissitudes of autumnal life–the lemon yellows and juicy oranges and passion reds and the few smug berry purples. And you are the pessimist that scratches without being heard, pessimist because you have no choice, because that wind cut off your stem that you held on to the branch with—you know you should have held on with a firmer grip—and now you’ll just change from green to brown. Your friends—so many of them!—up in the trees, don’t seem to notice your absence, that space where you occupied—was it this twig or that? You all will meet the same fate!, you shout up at them. But they are busy charming each other with a rosy red glow and outshining each other in sunny yellow. The wind rests you against the soil, and you accept: you’ll be the first among your friends to fertilize this tree, so it can grow tender buds in a spring you won’t see.

P.S. I fixed some stuff in the first lecture of 18.787 (see below post)—added an explanation of why $\mathbb{G}_{a,\text{Spec}(R)}(\text{Spec}(R'))$ is simply $(R',+)$, and why this sort of idea is important.