# Questions tagged [arithmetic-geometry]

A subject that lies at the intersection of algebraic geometry and number theory dealing with varieties, the Mordell conjecture, Arakelov theory, and elliptic curves.

468 questions
61 views

### Unipotent Groups and Torsors

I've been doing some reading in some arithmetic geometry, and there's a subtle point that is confusing me slightly: say $U$ is some unipotent affine group scheme over a field $L$, and $T$ is some ...
80 views

### Questions about Zeta Function of Singular Plane Curve

I am working on a project which involves learning about the zeta function (weil zeta function) for plane curves, but I do not know much algebraic geometry. (I do not know anything about schemes). I ...
31 views

### The set of the ideals of $\mathbb{C}$ corresponding to the points of complex geometry

There is parallel relation between the ideals over $\mathbb{C}$ corresponding to the points of complex geometry and the ideals of the field of the complex function, now how to construct the ideals ...
22 views

118 views

### Arithmetic intersection number

Let $\mathcal{X}$ be a smooth proper model of $X$ over $O_{K,S}$, where $K$ is a number field, $X$ is a projective curve over $K$, $O_{K,S}$ is the ring corresponding to the set $S$ of bad reductions ...
57 views

### Notation Confusion Reading Nick Katz' Proof of RH for (Projective, Smooth, Geometrically Connected) Curves

Trying to read this so-called "Note" by Nick Katz and cannot get over some of his notation. The fundamental group stuff is fine, but then he...seems to define some notation with the same notation in ...
406 views

### How can we use sin/cos for things like simple harmonic motion or any periodic type?

The sine and cosine functions are both well defined periodic function with fixed period and amplitude. My understanding is that for phenomena that are periodic, since sine and cosine are well defined ...
104 views

### Lifting points via étale morphism of adic spaces

This question was suggested to me during the reading of Huber's book about Etale Cohomology of Adic Spaces. I formulate this question here in the context of adic spaces, but I think, since a morphism ...
29 views

### Recursive writing involving arithmetic progression

I've been trying to figure out this recursion problem but I'm getting stuck trying to find the nth-term sequence for the last recursion. I found one but the second i'm so clueless about. I don't know ...
138 views

### field of rational functions of a curve

Let $C$ be the algebraic curve defined by the modular polynomial $\phi_N$ of order $N>1$ over the rational numbers, i.e. $$C:=\text{specm}(\mathbb{Q}[X,Y]/\phi_N(X,Y)).$$ ...
135 views