21 citations · 52 across the 20 of their papers we have counts for
20 papers
Derived Bockstein regulators and anticyclotomic -adic Birch and Swinnerton-Dyer conjectures
Takamichi Sano
We introduce "derived Bockstein regulators" by using an idea of Nekovář. We establish a general descent formalism involving derived Bockstein regulators. We give three applications…
On non-commutative Iwasawa theory and derivatives of Euler systems
David Burns, Takamichi Sano
We use the theory of reduced determinant functors from [24] to give a new, computationally useful, description of the relative -groups of orders in finite dimensional separabl…
On Euler systems for motives and Heegner points
Takenori Kataoka, Takamichi Sano
We formulate an Iwasawa main conjecture for a higher rank Euler system for a general motive. We prove "one half" of the main conjecture under mild hypotheses. We also formulate a c…
On -adic families of special elements for rank-one motives
Dominik Bullach, David Burns, Takamichi Sano
We conjecture that special elements associated with rank-one motives are obtained -adically from Rubin-Stark elements by means of a precise `higher-rank Soulé twist' constructio…
On derivatives of Kato's Euler system and the Mazur-Tate Conjecture
David Burns, Masato Kurihara, Takamichi Sano
We provide a new interpretation of the Mazur-Tate Conjecture and then use it to obtain the first (unconditional) theoretical evidence in support of the conjecture for elliptic curv…
On non-commutative Euler systems, I: preliminaries on `det' and `Fit'
David Burns, Takamichi Sano
We extend some classical constructions in commutative algebra to the setting of modules over orders in (non-commutative) semisimple algebras. Our theory incorporates, inter alia, `…
On functional equations of Euler systems
David Burns, Takamichi Sano
We establish precise relations between Euler systems that are respectively associated to a -adic representation and to its Kummer dual . Upon appropriate specializat…
On derivatives of Kato's Euler system for elliptic curves
David Burns, Masato Kurihara, Takamichi Sano
In this paper we study a new conjecture concerning Kato's Euler system of zeta elements for elliptic curves over . This conjecture, which we refer to as the `Genera…
On Euler systems for the multiplicative group over general number fields
David Burns, Alexandre Daoud, Takamichi Sano +1
We formulate, and provide strong evidence for, a natural generalization of a conjecture of Robert Coleman concerning Euler systems for the multiplicative group over arbitrary numbe…
On the theory of higher rank Euler, Kolyvagin and Stark systems, IV: the multiplicative group
David Burns, Ryotaro Sakamoto, Takamichi Sano
We describe a refinement of the general theory of higher rank Euler, Kolyvagin and Stark systems in the setting of the multiplicative group over arbitrary number fields. We use the…
On the theory of higher rank Euler, Kolyvagin and Stark systems, III: applications
David Burns, Ryotaro Sakamoto, Takamichi Sano
In an earlier article we proved the existence of a canonical Kolyvagin derivative homomorphism between the modules of Euler and Kolyvagin systems (in any given rank) that are assoc…
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 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 the theory of higher rank Euler, Kolyvagin and Stark systems
David Burns, Takamichi Sano
Mazur and Rubin have recently developed a theory of higher rank Kolyvagin and Stark systems over principal artinian rings and discrete valuation rings. In this article we describe…
On Stark elements of arbitrary weight and their -adic families
David Burns, Masato Kurihara, Takamichi Sano
We develop a detailed arithmetic theory related to special values at arbitrary integers of the Artin -series of linear characters. To do so we define canonical generalized Stark…
Iwasawa theory and zeta elements for
David Burns, Masato Kurihara, Takamichi Sano
We describe an explicit `higher rank' Iwasawa theory for zeta elements associated to the multiplicative group over abelian extensions of general number fields. We then show that th…
On zeta elements for
David Burns, Masato Kurihara, Takamichi Sano
In this paper, we present a unifying approach to the general theory of abelian Stark conjectures. To do so we define natural notions of `zeta element', of `Weil-étale cohomology co…
On a conjecture for Rubin-Stark elements in a special case
Takamichi Sano
We prove a conjecture on Rubin-Stark elements, which was recently proposed by the author, and also by Mazur and Rubin, in a special case.
Refined abelian Stark conjectures and the equivariant leading term conjecture of Burns
Takamichi Sano
We formulate a conjecture which generalizes Darmon's "refined class number formula". We discuss relations between our conjecture and the equivariant leading term conjecture of Burn…
A generalization of Darmon's conjecture for Euler systems for general p-adic representations
Takamichi Sano
Darmon's conjecture on a relation between cyclotomic units over real quadratic fields and certain algebraic regulators was recently solved by Mazur and Rubin by using their theory…