Galois groups and complex multiplication
نویسندگان
چکیده
منابع مشابه
Galois Groups and Complex Multiplication
The Schur problem for rational functions is linked to the theory of complex multiplication and thereby solved. These considerations are viewed as a special case of a general problem, prosaically labeled the extension of constants problem. The relation between this paper and a letter of J. Herbrand to E. Noether (published posthumously) is speculatively summarized in a conjecture that may be reg...
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Let G be a complex reflection group and K its field of definition (the subfield of C generated by the reflection character). We show that Gal(K/Q) injects into the group A of outer automorphisms of G which preserve reflections, and that this injection with a few exceptions can be chosen such that it commutes with the Galois action on characters of G; further, replacing if needed K by an extensi...
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The smallest non-abelian p-groups play a fundamental role in the theory of Galois p-extensions. We illustrate this by highlighting their role in the definition of the norm residue map in Galois cohomology. We then determine how often these groups — as well as other closely related, larger p-groups — occur as Galois groups over given base fields. We show further how the appearance of some Galois...
متن کاملGalois Groups as Permutation Groups
Writing f(T ) = (T − r1) · · · (T − rn), the splitting field of f(T ) over K is K(r1, . . . , rn). Each σ in the Galois group of f(T ) over K permutes the ri’s since σ fixes K and therefore f(r) = 0⇒ f(σ(r)) = 0. The automorphism σ is completely determined by its permutation of the ri’s since the ri’s generate the splitting field over K. A permutation of the ri’s can be viewed as a permutation ...
متن کاملGalois Groups and Greenberg’s Conjecture
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1978
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1978-0472917-6