Introduction to the Construction of Class FieldsCUP Archive, 1985/08/30 - 213 ページ 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. |
目次
Early versions of class field theory | 8 |
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 |
Exercises | 204 |
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多く使われている語句
abelian algebraic assume basis called Chapter characters class field class group class number complex concept condition conjugates consider construction Corollary corresponding course cyclic defined Definition denoted determined discriminant divides divisible divisors elements equation equivalent Exercise exists expressed extension fact factors finite follows function fundamental genus given hence Hilbert ideal ideal class Illustration integer invariant leads Lemma mapping matrices maximal means modular modulo multiplicative norm normal Note period points poles polynomial positive prime primitive principal Proof prove quadratic ramified rational references relation relative Remark replaced represented residue result Riemann ring class field roots satisfies splits structure subfields subgroup surface symbol Theorem theory tower transfer transformations unique unit unramified values variable Verify write