Field Arithmetic

In mathematics, field arithmetic is a subject that studies the interrelations between arithmetic properties of a field and its absolute Galois group. It is an interdisciplinary subject as it uses tools from algebraic number theory, arithmetic geometry, algebraic geometry, model theory, the theory of finite groups and of profinite groups.

Read more about Field Arithmetic:  Fields With Finite Absolute Galois Groups, Fields That Are Defined By Their Absolute Galois Groups, Pseudo Algebraically Closed Fields

Famous quotes containing the words field and/or arithmetic:

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    I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgments and consequently a priori. Arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts; calculation becomes deduction.
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