Sheaf (Čech) Cohomology: A glimpse

This is a blogpost on Sheaf Cohomology. We shall be following this article. If the reader wants to read up on what a sheaf is, he/she can read the very readable wikipedia article on it. From the word cohomology, we can guess that we shall be talking about a complex with abelian groups and boundaryContinue reading “Sheaf (Čech) Cohomology: A glimpse”

Sheafification

This is a blog post on sheafification. I am broadly going to be following Ravi Vakil’s notes on the topic. Sheafification is the process of taking a presheaf and giving the sheaf that best approximates it, with an analogous universal property. In a previous blog post, we’ve discussed examples of pre-sheaves that are not sheaves.Continue reading “Sheafification”

Nakayama’s lemma

The Nakayama lemma as a concept is present throughout Commutative Algebra. And truth be told, learning it is not easy. The proof contains a small trick that is deceptively simple, but throws off many people. Also, it is easy to dismiss this lemma as unimportant. But as one would surely find out later, this wouldContinue reading “Nakayama’s lemma”