Artin symbol

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- Tags: - #NT/algebraic - Refs: - #todo/add-references - Links: - Unsorted/ramification index - congruence subgroup - arithmetic Frobenius - Kronecker symbol. - class field theory


Artin symbol

attachments/Pasted%20image%2020220124100104.png attachments/Pasted%20image%2020220126162507.png # Artin Map attachments/Pasted%20image%2020220124100224.png

attachments/Pasted%20image%2020220126162728.png

Example: \({ {\mathbf{Q}}_p }\)

attachments/Pasted%20image%2020220408133239.png

attachments/Pasted%20image%2020220408133357.png attachments/Pasted%20image%2020220408133424.png

Artin Reciprocity

Statement of Artin reciprocity: the Artin map is surjective. attachments/Pasted%20image%2020220126164003.png attachments/Pasted%20image%2020220126164030.png

attachments/Pasted%20image%2020220126170059.png attachments/Pasted%20image%2020220126214037.png

Global Artin Map

attachments/Pasted%20image%2020220127134539.png

Examples

attachments/Pasted%20image%2020220126232933.png

Links to this page
#NT/algebraic #todo/add-references