---
date: 2021-03-26
tags: [ web/quick-notes ]
---


# 2021-03-26

## 20:00

![](attachments/image_2021-03-26-20-00-58.png)

- What is a [Dirichlet character](Dirichlet%20character)?

	- A Dirichlet character is equivalent to a group homomorphism
\[
\chi:(\mathbb{Z} / N)^{\times} \rightarrow \mathbb{C}^{\times}
.\]

- What is a [Dirichlet L function](Dirichlet%20L%20function)?
	- Definition of a Dirichlet $L\dash$function:

\[
L(s ; \chi):=\sum_{n=1}^{\infty} \frac{\chi(n)}{n^{s}}
=\prod_{p} \qty{ 1-\chi(p) p^{-s} }^{-1}
.\]

- How is a [Bernoulii number](Bernoulii%20number) defined?
	Generalized Bernoulli numbers:

	![](attachments/image_2021-03-26-20-03-27.png)

- What is the [conductor](conductor.md) of a [Dirichlet character](Dirichlet%20character)?

- What is the [J-homomorphism](J-homomorphism.md)?
	- How is it defined in terms of [loop space](loop%20space.md)?
	- How is it defined in terms of [framed cobordism](framed%20cobordism)?
	  What is a [framing](framed.md)?
	- How is it defined in terms of[Thom space](Thom%20space.md)?
	  	What is a Thom space?

		![](attachments/image_2021-03-26-20-04-44.png)	

- What is a [complex oriented cohomology theory](complex%20oriented%20cohomology%20theory.md)?

	![](attachments/image_2021-03-26-20-06-00.png)

- What is a [uniformizer](uniformizer)?
  - Uniformizer $\pi$: can think of this as a generator of a maximal ideal.