0
votes
0answers
422 views

A letter from J. P. Serre

Which is the letter where J. P. Serre present "Analogues Kählériens de certaines conjectures de Weil" to Weil?
4
votes
2answers
282 views

Time-line until the publicaton of Weil of “Numbers of solutions of equations in finite fields”

In "On the history of the Weil Conjectures" Dieudonné says: "Appropriately enough, the story, as with so many problems in number theory, begins with Gauss...". C. F. Gauss, Disquisitiones ...
19
votes
9answers
2k views

What are some interesting problems in the intersection of Algebraic Number Theory and Algebraic Topology?

I'm a beginning graduate student and while my background is primarily in algebraic number theory, I've found myself a bit smitten with the subject of algebraic topology recently after only having read ...
24
votes
3answers
2k views

Why aren't there more classifying spaces in number theory?

Much of modern algebraic number theory can be phrased in the framework of group cohomology. (Okay, this is a bit of a stretch -- much of the part of algebraic number theory that I'm interested ...
17
votes
3answers
660 views

What's the analogue of the Hilbert class field in the following analogy?

There's a wonderful analogy I've been trying to understand which asserts that field extensions are analogous to covering spaces, Galois groups are analogous to deck transformation groups, and ...