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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

7 votes
1 answer
518 views

How to prove local class field theory from global class field theory

Historically (as I gather from Learning Class Field Theory: Local or Global First?), global class field theory was proved first, and then used to deduce local class field theory. But nowadays most tre …
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13 votes
0 answers
478 views

The trace formula over function fields

There are many examples in number theory where an "arithmetic" problem (i.e. for number fields) has an easier analogue for function fields over finite fields. This is also true for questions surroundi …
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