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Bounded realization of l-groups over global fields

  • Wulf-Dieter Geyer (a1) and Moshe Jarden (a2)

Abstract.

We use the method of Scholz and Reichardt and a transfer principle from finite fields to pseudo finite fields in order to prove the following result. THEOREM Let G be a group of order ln, where l is a prime number. Let K 0 be either a finite field with |K 0| > l 4n+4 or a pseudo finite field. Suppose that l ≠ char(K 0) and that K 0 does not contain the root of unity ζl of order l. Let K = K 0(t), with t transcendental over K 0. Then K has a Galois extension L with the following properties: (a) (L/K) ≅ G; (b) L/K 0 is a regular extension; (c) genus(L) < ; (d) K 0[t] has exactly n prime ideals which ramify in L; the degree of each of them is [K 0 : K 0]; (e) (t) totally decomposes in L; (f) L = K(x), with and deg(ai (t)) < deg(a 1(t)) for i = 1,…,ln .

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References

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Bounded realization of l-groups over global fields

  • Wulf-Dieter Geyer (a1) and Moshe Jarden (a2)

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