Introduction to the Construction of Class Fields

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CUP Archive, 30.08.1985 - 213 Seiten
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In this graduate level textbook, Professor Cohn takes a problem that Pythagoras could have posed, and using it as motivation, develops a constructional introduction to classical field theory and modular function theory. The interest in constructional techniques has increased recently with the advent of cheap and plentiful computer technology. The beginning chapters provide the motivation and necessary background in elementary algebraic number theory and Riemann surface theory. The ideas and results are then applied and extended to class field theory. In the later chapters, more specialized results are presented, with full proofs, though the author emphasizes, with examples, the relation of the material to other parts of mathematics.
 

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Inhalt

Early versions of class field theory
6
Interpretation by rings and ideals
24
Finite invariants of a field
39
Function fields
58
Relative fields
79
The WHAT theorem of class field theory
96
The genus class field and transfer theory
112
Class fields by radicals
132
The modular function field
153
Class fields by modular functions
178
References
206
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