Comments for A Mind for Madness

Comment on Gauss-Manin Connection 1 by Serre-Tate Theory 2 | A Mind for Madness

Serre-Tate Theory 2 | A Mind for Madness — Tue, 18 Jun 2013 22:06:56 +0000

[…] cohomology of the family that is adapted to the Hodge filtration such that in these coordinates the Gauss-Manin connection has an explicit and nice […]

Comment on What’s up with the fppf site? by Serre-Tate Theory 2 | A Mind for Madness

Serre-Tate Theory 2 | A Mind for Madness — Tue, 18 Jun 2013 22:06:53 +0000

[…] . Last time we said the main theorem was that this map is an isomorphism. To tie this back to the flat topology stuff, is the group representing the functor […]

Comment on Deformations of p-divisible Groups by Serre-Tate Theory 1 | A Mind for Madness

Serre-Tate Theory 1 | A Mind for Madness — Mon, 10 Jun 2013 05:07:08 +0000

[…] Today we’ll try to answer the question: What is Serre-Tate theory? It’s been a few years, but if you’re not comfortable with formal groups and -divisible groups, I did a series of something like 10 posts on this topic back here: formal groups, p-divisible groups, and deforming p-divisible groups. […]

Comment on Heights of p-divisible Groups by Serre-Tate Theory 1 | A Mind for Madness

Serre-Tate Theory 1 | A Mind for Madness — Mon, 10 Jun 2013 05:07:06 +0000

[…] groups, I did a series of something like 10 posts on this topic back here: formal groups, p-divisible groups, and deforming p-divisible […]

Comment on Formal Groups 1 by Serre-Tate Theory 1 | A Mind for Madness

Serre-Tate Theory 1 | A Mind for Madness — Mon, 10 Jun 2013 05:07:04 +0000

[…] groups and -divisible groups, I did a series of something like 10 posts on this topic back here: formal groups, p-divisible groups, and deforming p-divisible […]

Comment on Towards Stacks 1 by What’s up with the fppf site? | A Mind for Madness

What’s up with the fppf site? | A Mind for Madness — Thu, 06 Jun 2013 01:58:43 +0000

[…] turns out that you can switch to a finer topology called the fppf topology (or site). This is similar to the étale site, except instead of making your covering families using étale […]

Comment on Intro to Brauer Groups by What’s up with the fppf site? | A Mind for Madness

What’s up with the fppf site? | A Mind for Madness — Thu, 06 Jun 2013 01:58:41 +0000

[…] without a doubt you’ve encountered étale cohomology. In fact, I’ve used it tons on this blog already. Here’s a standard way in which it comes up. Suppose you have some (smooth, […]

Comment on Projective Modules over Dedekind Domains by Qiaochu Yuan

Qiaochu Yuan — Fri, 10 May 2013 23:48:22 +0000

I'm not sure how to deal with this either. I posted a math.SE question.

Comment on Projective Modules over Dedekind Domains by hilbertthm90

hilbertthm90 — Fri, 10 May 2013 22:48:22 +0000

Ah yes. Good catch. We definitely can’t just pick some arbitrary , but we are allowed to pick it however we want. I think I was following J. P. May’s notes on this and he just says choose elements of that span an -dimensional subspace of . Again, that doesn’t seem good enough because by seems to satisfy that but still leaves torsion.

I feel like I had something in mind when I wrote this, but I can’t remember now.

Comment on Projective Modules over Dedekind Domains by Qiaochu Yuan

Qiaochu Yuan — Fri, 10 May 2013 21:31:55 +0000

I don’t understand a step in your proof of the structure theorem. It doesn’t seem to be true in general that a rank module is necessarily projective, since e.g. it need not be torsion-free. So how do you know that is torsion-free?