All Questions

What are nice applications of Tate-Poitou duality?

If someone asked me the question for the fundamental group, I would answer as follows: The connection to classification of covering spaces. The fundamental group of many spaces is an object of ...

Automorphic forms are ubiquitous in modern number theory and stands as a mysterious Graal lying at the intersection of many fields, if not building valuable bridges between them. However, since this ...

One of the difficulties of mathematics over other sciences is that our problems are harder to motivate to a general audience. A biologist studying a particular pathway in the body can say that he's ...

This is, basically, me trying to generalize "Why should I care for sheaves and schemes?" into a reasonable question. Whether successfully, time will tell, but let me hope that if not the question, ...