In question #7656, Peter Arndt asked why the Gamma function completes the Riemann zeta function in the sense that it makes the functional equation easy to write down. Several of t …

I've heard of this many times, but I don't know anything about it. What I do know is that it is supposed to solve the problem of the fact that the final object in the category of …

Homological algebra for abelian groups is a standard tool in many fields of mathematics. How much carries over to the setting of commutative monoids (with unit)? It seems like ther …

Minhyong Kim's reply to a question John Baez once asked about the analogy between $\text{Spec } \mathbb{Z}$ and 3-manifolds contains the following snippet: Finally, regarding the …

Is there an notion of elliptic curve over the field with one element? As I learned from a previous question, there are several different versions of what the field with one elemen …

In a workshop about the geometry of $\mathbb{F}_1$ I attended recently, it came up a question related to a mysterious but "not-so-secret-anymore" seminar about... an hypothetical T …

If doing geometry over Fp means also using its algebraic closure, it must be interesting to talk about the algebraic closure of F_1 - the field with one element. I saw that the fi …

In Connes work on the Riemann Hypothesis he talks about constructing $\overline{\text{Spec}\mathbb{Z}}$ as a curve over the field with one element. I just want to know what Spec me …

I repeatedly heard that K(F_1) is the sphere spectrum. Does anyone know about the proof and what that means?

What should be $\text{Spec } \mathbb{Z}[\sqrt{D}] \times_{\mathbb{F}_1} \text{Spec } \overline{\mathbb{F}}_{1}$? Sure, there's more than one definition. I'm looking for any answer …