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On meromorphic functions defined by a differential system of order 1

Tristan Torrelli (2004)

Bulletin de la Société Mathématique de France

Given a germ h of holomorphic function on ( n , 0 ) , we study the condition: “the ideal Ann 𝒟 1 / h is generated by operators of order1”. We obtain here full characterizations in the particular cases of Koszul-free germs and unreduced germs of plane curves. Moreover, we prove that this condition holds for a special type of hyperplane arrangements. These results allow us to link this condition to the comparison of de Rham complexes associated with h .

On non-commutative twisting in étale and motivic cohomology

Jens Hornbostel, Guido Kings (2006)

Annales de l’institut Fourier

This article confirms a consequence of the non-abelian Iwasawa main conjecture. It is proved that under a technical condition the étale cohomology groups H 1 ( 𝒪 K [ 1 / S ] , H i ( X ¯ , p ( j ) ) ) , where X Spec 𝒪 K [ 1 / S ] is a smooth, projective scheme, are generated by twists of norm compatible units in a tower of number fields associated to H i ( X ¯ , p ( j ) ) . Using the “Bloch-Kato-conjecture” a similar result is proven for motivic cohomology with finite coefficients.

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