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Titlebook: Galois Theory and Modular Forms; Ki-ichiro Hashimoto,Katsuya Miyake,Hiroaki Nakamur Book 2004 Kluwer Academic Publishers 2004 Abelian vari

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On the Essential Dimension of ,-GroupsWe improve the known bounds on the essential dimension of .-groups over (large) fields of characteristic ..
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On the Non-Existence of Certain Galois ExtensionsIn this article, we give a survey of my results on the non-existence and finiteness of certain Galois extensions of the rational number field ℚ with prescribed ramification. The detail has been (will be) published in [8], [9], [10], [11], [12].
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Frobenius Modules and Galois GroupsIn these notes some basic facts on Frobenius modules are collected. Frobenius modules are finite-dimensional vector spaces over fields with a Frobenius endomorphism Ø, provided with an injective Ø-semilinear Frobenius operator Ф.
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Projektauftrag und Projektabwicklung, inverse Galois problem. Especially the case when . = . the rational number field, plays an important role in the study of the absolute Galois Group of .. By many mathematicians, the existence of ./.-extensions has been shown for a lot of finite groups . by now (cf. Malle-Matzat [14], Serre [19], etc.)
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E. Blanck,H. Niklas,Br. Tacke,F. Gieseckeelds of their genus fields. More precisely, under GRH, among the 305 imaginary quadratic number fields with discriminants larger than —1000, at most 16 fields are exceptional [39], [40], and among the 1690 real quadratic number fields with discriminants less than or equal to 5565, only 4 fields are exceptional [41].
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