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Non-abelian Stark-type conjectures

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Let L/K be a finite Galois extension of number fields with Galois group G. We use leading terms (resp. values) of Artin L-series at strictly negative integers (resp. at zero) to construct elements which we conjecture to lie in the annihilator ideal associated to the Galois action on the higher dimensional algebraic K-groups of the ring of integers in L (resp. on the class group of L). For abelian G our conjectures coincide with conjectures of Snaith and Brumer, and thus generalize also the well known Coates-Sinnott conjecture. We discuss how they are related to the equivariant Tamagawa number conjecture and provide some non-conjectural evidence for our conjectures.

This talk is part of the Number Theory Seminar series.

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