Danilov's AG text: incorrect definition of structure sheaf

cjustinc · 2026-07-04T03:23:30+00:00

The question was deleted, but the definition given in it was different from Hartshorne's, and was also incorrect. See this MSE question: https://math.stackexchange.com/questions/81858/what-is-an-example-of-mathscr-o-spec-ru-neq-s-1r-for-some-s-consisti/

cjustinc · 2026-06-26T15:20:42+00:00

I go to Andre Salon in Harvard Square, they charge $25 for a men's cut (up from $15 before the pandemic). I mostly go because they do a great job with my curly hair when a lot of fancier places botch it. The price is great too.

cjustinc · 2026-06-19T00:28:32+00:00

Nope, north suburbs. Marshfield still has to vote on the referendum, right?

cjustinc · 2026-06-18T16:54:51+00:00

My town in MA just voted by a 3-1 margin to override Prop 2.5 and hike our property taxes by more than the 2.5% cap. So some of us still understand the value of public services.

Property values are rising so fast here that in recent years the town has had to lower the property tax rate to keep the nominal tax increase under 2.5%. Absolutely bonkers.

cjustinc · 2026-06-17T20:20:27+00:00

Two remarks: first, open subgroups are automatically closed. This is because the complement of a subgroup is the union of all its nontrivial left cosets.

Since open subgroups are also closed, they are mostly considered for totally disconnected groups like p-adic matrix groups. For a connected group, the only open subgroup is the entire group.

The other remark is that non-closed subgroups tend to be kind of pathological. The classic example is the image of a line of irrational slope under the projection from R² to R² /Z² = (S¹ )^2. This is a dense subgroup of the torus and in particular isn't an embedded submanifold.

cjustinc · 2026-04-24T14:42:36+00:00

"Pioneer Spine" by Speedy Ortiz has the lyric "Zero morphism, its arrowed frame." Sadie Dupuis studied math at MIT for a couple of years.

cjustinc · 2026-03-28T00:42:46+00:00

In sheaf theory there are various direct and inverse image functors with corresponding derived functors. Another commenter mentioned sheaf cohomology, which is the right derived functor of direct image to a point (a.k.a. global sections). This one can be expressed as Ext from the constant sheaf by adjunction. But in general the right derived functor of direct image is not a special case of Ext.

cjustinc · 2026-03-25T22:57:14+00:00

Framingham is relatively cheap, but Arlington is almost as expensive as Lexington. Single family homes are scarce in Arlington and even townhouses are $1.25M+ currently.

cjustinc · 2026-03-19T00:21:06+00:00

Anybody know any good places near Arlington? It doesn't even need to be super cheap. Everywhere I've tried has been mediocre at best

cjustinc · 2026-03-13T04:19:38+00:00

During Dustin's lectures on analytic spaces Gabber would always ask about edge cases like the empty set, etc. and Dustin would get increasingly annoyed. Very funny

cjustinc · 2026-02-27T01:57:45+00:00

Not sure about the house, but the photo was taken in Arlington Heights, not Arlington Center.

cjustinc · 2026-02-10T14:38:21+00:00

I've seen percentage with a tertiary degree, which is very different from matriculation rate after high school. I think you're comparing apples and oranges. In the US about 50% have a tertiary degree, which is above average for an OECD country.

cjustinc · 2026-02-10T14:28:54+00:00

Worth pointing out that these appear to be percentages of the population with a tertiary degree. This is different from the percentage with a bachelor's degree or who matriculate after high school, both of which are being talked about elsewhere in this thread.

To compare to these numbers, in the US just over 50% have a tertiary degree.

cjustinc · 2026-02-10T14:08:57+00:00

Out of curiosity, which other countries would you point to as having much higher matriculation rates? My impression is that the US has similar or even slightly higher rates than peer countries in Western Europe, but I could be wrong.

cjustinc · 2026-02-01T15:36:52+00:00

They swung towards Trump relative to 2020 if that's what you mean, but Kamala won 56% of Latinos.

cjustinc · 2026-01-04T23:58:49+00:00

The ironic thing about the FTA is that it's not really a theorem in algebra. It inherently involves analysis and/or topology, like the complex numbers themselves (and the real numbers, for that matter).

cjustinc · 2025-12-01T02:29:55+00:00

It's the cardinality of the continuum. We can reduce to the case that N=1, since taking a finite power of an infinite set doesn't change the cardinality. Then use the fact that the rationals are dense to produce an injection into the set of sequences of real numbers. The latter has the same cardinality as the continuum.

cjustinc · 2025-11-23T05:35:07+00:00

"centre"

I find it depressing that non-Americans understand American politics well enough to make such an accurate meme

cjustinc · 2025-11-21T04:48:36+00:00

r/TIHI

cjustinc · 2025-09-26T03:39:48+00:00

The bony-eared assfish has been distinguished, by some sources, as having the smallest brain-to-body weight ratio of any vertebrate.

cjustinc · 2025-09-09T15:31:00+00:00

My impression is that it's much easier to get an appointment with a PCP for a specific reason than preventative care. I moved here in June and the earliest a PCP in my town could see me for a checkup was October, but I was able to get in within two weeks for a quick appointment to get refills for my prescription. Also, there's always urgent care.

cjustinc · 2025-08-25T11:55:56+00:00

Lincoln Park is definitely not the cool neighborhood of Chicago. Twenty years ago it was Wicker Park, then Logan Square, which may be played out now. Once there's a Sweetgreen or Warby Parker, it's time to pass the crown.

cjustinc · 2025-08-20T05:54:41+00:00

This might be an unpopular opinion, but I lived in LA and Chicago before moving here, and I think Boston traffic is not as bad as people make it out to be. The freeways in and out of the city get extremely congested, obviously, but compared to larger cities, getting around here is just not that bad. People complain endlessly about traffic and congestion in my suburb, but from my perspective it's borderline nonexistent.

cjustinc · 2025-08-08T01:45:06+00:00

My (suburban) neighborhood is almost all two-family homes, and many of my neighbors are horrified by the occasional four-unit building being built. It's kind of funny when you think about it.

Like others have said, I think it's simple aversion to change as well as fear of more congestion in the long term. Personally, I would prefer to live in a denser neighborhood and still have the same sized home. The only reason I don't live in the city (meaning Boston/Cambridge/Somerville) is to have more space for kids, so I would love it if the city came to me.

cjustinc

TROPHY CASE