Ranks of elliptic curves in cubic extensions
A remark on Tate's algorithm and Kodaira types
We remark that Tate’s algorithm to determine the minimal model of an elliptic curve can be stated in a way that characterises Kodaira types from the minimum of . As an application, we deduce the behaviour of Kodaira types in tame extensions of local fields.
Elliptic curves with all quadratic twists of positive rank
Brauer relations in finite groups
If is a non-cyclic finite group, non-isomorphic -sets may give rise to isomorphic permutation representations . Equivalently, the map from the Burnside ring to the rational representation ring of has a kernel. Its elements are called Brauer relations, and the purpose of this paper is to classify them in all finite groups, extending the Tornehave–Bouc classification in the case of -groups.
Computing special values of motivic -functions.
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