Inverse Galois Theory

By Gunter Malle, B. H. Matzat. 2002

326 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/2bcb24b75f1d7fa5fefd93ab050c57421329f90e

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In Computational Mechanics

Citations in the corpus

The rational function analogue of a question of Schur and exceptionality of permutation representations (2002, background): “gidity criterion in order to prove existence of certain regular extensions E|K(t) with given ramiﬁcation structure and geometric monodromy group. The main reference of the material in this section is [MM99] and [V¨ol96]. Deﬁnition 2.6. Let Gbe a ﬁnite group, and H = (C1,C2,...,Cr) be an r– tuple of ”
Elliptic Subfields and Automorphisms of Genus 2 Function Fields (2001, methodology): “This allows us to compute the cardinality of S j ( n ) for n  21, using a random search to ﬁnd the triples and the structure constant formula [22], Prop.”
Resolution of singularities and modular Galois theory (2000, background): “Eventually I may aspire to enter the rarefied atmosphere of his [Th1], [Th2], as well as MatzatMalle’s [MMa] and Voelklein’s [Vo1], [Vo2], characteristic zero Galois theory work.”
On the ‘Section Conjecture’ in anabelian geometry (2003, background): “If char K > 0 and nX f 1, then p1ðXKÞ is no longer free, but still projective ([MM], V.”
Counting nilpotent Galois extensions (2001, unknown): “By the Theorem of Kochendörffer [12], Thm. IV.8.2, a solution field L/k to the original embedding problem can be found inside the Galois closure of L̃/k.”
On the representation theory of Iwahori-Hecke algebras of extended finite Weyl groups (2000, background): “For applications to certain problems arising in inverse Galois theory, see [28, 29].”
Motives with exceptional Galois groups and the inverse Galois problem (2011, background): “A lot of finite simple groups are proved to be Galois groups over Q, see [29] and [37], yet the problem is still open for many finite simple groups of Lie type.”
Patching and Galois Theory (2003, background): “See the books [Se7], [Vö], and [MM] for much more about rigidity.”
On the trigonometric moment problem (2011, methodology): “Given a set of k generators of the group and for each generator a ramification point on the Riemann sphere, we can invoke Riemann’s Existence Theorem to guarantee that this monodromy group is realizable by an algebraic function which is ramified at exactly these points, and whose monodromy around th”