John Tate’s works
I’ve been sick for a couple of days. So I decided to take the evening off and read random articles on the internet. I chanced upon Milne’s 9 page summary of Tate’s collected works.
I was indeed surprised by how comprehensible it was. John Tate passed away recently. Hence, it is only appropriate that one tries to fathom his contributions to Mathematics.
Some things that struck me were Tate’s conjecture, which is pretty similar to the Hodge conjecture, and the Isogeny theorem, which is what a grad school friend of mine works on (I think she is working on a slightly generalized version of it though, in a different context).
Of all the fields of Mathematics that I have been exposed to, number theory has always seemed the farthest from comprehension. Although one would imagine that a subject purportedly dealing with natural numbers would be comprehensible, the modern treatment of the field often seems to be written in a different language: what with its Hecke L-functions and number fields and unramified extensions and the like. This article, I feel, attempts to bridge that divide. I am truly grateful for the expository gift of Milne.