# Tag Info

### Visualizing $\textbf{Q}_p$ vs. $\textbf{F}_p((t))$?

Let's visualize the fragments $\mathbf Z_p$ and $\mathbf F_p[[t]]$ instead, since they're compact, and focus only on their structure as abelian topological groups. Then the left figure is $\mathbf Z_3$...
• 27k

### What is a Shimura variety and why should I care about them?

This sounds a lot more appropriate for MO than MSE, and, to be honest, as I don’t know very much about Shimura varieties, I’d like an authoritative answer myself. I think the broad idea of what ...
• 35.2k

### I would like to determine if exists a polynomial $R$ with integer coefficients such that $P(x)=Q(R(x))$.

Todd Cochrane's article The Diophantine Equation $f(x) = g(y)$ provides a theorem which guarantees existence of a rational polynomial $R(x)$. Specifically if \begin{align} P(x) \equiv a_nx^n&+a_{n-...
• 17k
Accepted

• 2,441

### Gauss circle problem : a simple asymptotic estimation.

Pick a square with unit side length centered at every lattice point inside the region $x^2+y^2=n^2$, i.e. the circle with radius $n$ centered at the origin. Those squares entirely cover the circle ...
• 356k

### Lang-Nishimura theorem still carries through or fails when assumptions are dropped?

The theorem of Lang-Nishimura can fail if either of the aforementioned changes is made. The assumption that $Y$ is proper is dropped. Let $k$ be a finite field. Let $X = \mathbb{A}_k^1$, which is ...
• 1,432

### Derived category and so on

There are two "families" of derived categories people study in algebraic geometry: derived categories of (quasi-)coherent sheaves on a (locally noetherian) scheme and derived categories of ...
• 3,253

### Why is the fundamental group a sheaf in the etale topology?

In this case, it is indeed an action rather than an outer action, since a splitting has been chosen using the base point. It is a classical fact that a sheaf is the same as a set with Galois action. ...
• 2,160
Accepted

### What is the motivation behind the Hilbert Symbol?

The following relates more to Number Theory than Geometry, but for what it's worth the Hilbert symbol can be associated with an element of order 2 in the Brauer group of a number field $K$ thus ...
• 4,937
Accepted

### Grothendieck's Vanishing Cycles

The analogy with the classical picture is the following : A small disk around $x$ is the spectrum $\tilde{S}$ of a strict henselization $\mathcal{O}_{C,x}^{sh}$ of $\mathcal{O}_{C,x}$ The point $x$ ...
• 12.7k

### Visualizing $\textbf{Q}_p$ vs. $\textbf{F}_p((t))$?

You’ve contacted me directly, perhaps guessing (correctly) that I missed this question. Before I explain my general lack of a picture for the $p$-adics and the rings $\Bbb F_q[[t]]$, maybe I should ...
• 63.4k