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Семинар по арифметической геометрии
21 февраля 2022 г. 15:00–17:00, г. Москва, МИАН, комн. 303 (ул. Губкина, 8)
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Ramification theory and Artin Represenration
В. А. Левашев |
Количество просмотров: |
Эта страница: | 137 |
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Аннотация:
For every finite Galois extension of a local separable field we can constuct ramification groups $G_{i}$. It is clear from definition that these groups behave well under taking subgroups of the Galois group $G$, but the same is not true for taking quotients of $G$. I will try to explain how we can define upper-numbering $G^{i}$ which will behave well under taking quotients.
After this, I will give a construction of an Artin character. A non-obvious fact is that it is a character of a linear representation. I will give a plan of the proof of this fact and at the end we will discuss some application of this theory to number fields.
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