Equivariant epsilon constant conjectures for weakly ramified extensions

Bley, Werner and Cobbe, Alessandro (2016): Equivariant epsilon constant conjectures for weakly ramified extensions. In: Mathematische Zeitschrift, Vol. 283, No. 3-4: pp. 1217-1244

Abstract

We study the local epsilon constant conjecture as formulated by Breuning in Breuning (J London Math Soc 70(2):289-306, 2004). This conjecture fits into the general framework of the equivariant Tamagawa number conjecture (ETNC) and should be interpreted as a consequence of the expected compatibility of the ETNC with the functional equation of Artin-L-functions. Let be unramified. Under some mild technical assumption we prove Breuning's conjecture for weakly ramified abelian extensions N / K with cyclic ramification group. As a consequence of Breuning's local-global principle we obtain the validity of the global epsilon constant conjecture as formulated in Bley and Burns (Proc Lond Math Soc 87(3):545-590, 2003) and of Chinburg's -conjecture as stated in Chinburg (Ann Math 121(2):351-376, 1985) for certain infinite families F / E of weakly and wildly ramified extensions of number fields.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0025-5874
• Language: English