21 citations · 89 across the 29 of their papers we have counts for
4 papers · 1 filter
On higher special elements of -adic representations
David Burns, Takamichi Sano, Kwok-Wing Tsoi
As a natural generalization of the notion of `higher rank Euler system', we develop a theory of `higher special elements' in the exterior power biduals of the Galois cohomology of…
On refined metric and hermitian structures in arithmetic, I: Galois-Gauss sums and weak ramification
Werner Bley, David Burns, Carl Hahn
We use techniques of relative algebraic K-theory to develop a common refinement of the existing theories of metrized and hermitian Galois structures in arithmetic. As a first appli…
On the theory of higher rank Euler, Kolyvagin and Stark systems, II
David Burns, Ryotaro Sakamoto, Takamichi Sano
We prove the existence of a canonical `higher Kolyvagin derivative' homomorphism between the modules of higher rank Euler systems and higher rank Kolyvagin systems, as has been con…
On a refinement of the Birch and Swinnerton-Dyer Conjecture in positive characteristic
David Burns, Mahesh Kakde, Wansu Kim
We formulate a refined version of the Birch and Swinnerton-Dyer conjecture for abelian varieties over global function fields. This refinement incorporates both families of congruen…