---
date: 2022-02-23 18:30
modification date: Wednesday 23rd February 2022 18:30:27
title: functor of points
aliases: [functor of points]

---


---

- Tags 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- [scheme](Unsorted/scheme.md)

---

# functor of points

For [schemes](Unsorted/scheme.md):
![](attachments/Pasted%20image%2020220321110856.png)

# Examples

- $F(R) = R^n$ is $\AA^n$ represented by $k[x_1,x_2,\cdots, x_n]$.
- $F(R) = R\units$ is $\GG_{m}$, represented by $k[x,x\inv]$.
	- This is the diagonal group scheme for $\ZZ$.
- $F(R) = (R, +)$ is $\GG_{a}$, represented by $k[x]$.
- $F(R) = \ts{x\in R \st x^n=1}$ is $\mu_{n}$, represented by $k[x]/(x^n-1)$.
	- This is the diagonal group scheme for $C_n$.
- $F(R) = \kalg(k, R)$ is $\spec k$.

![](attachments/Pasted%20image%2020220315152218.png)
![](attachments/Pasted%20image%2020220315152233.png)
![](attachments/Pasted%20image%2020220315152246.png)