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of 34
pro vyhledávání: '"Castillo, Daniel Macias"'
The theory of Weil-Stark elements is used to develop an axiomatic approach to the formulation of refined versions of Stark's Conjecture. This gives concrete new results concerning leading terms of Artin $L$-series and arithmetic properties of Stark e
Externí odkaz:
http://arxiv.org/abs/2310.10581
We derive new cases of conjectures of Rubin and of Burns--Kurihara--Sano concerning derivatives of Dirichlet $L$-series at $s = 0$ in $p$-elementary extensions of number fields for arbitrary prime numbers $p$. In naturally arising examples of such ex
Externí odkaz:
http://arxiv.org/abs/2310.10468
Let $K/k$ be a finite Galois extension of global function fields. Let $E$ be a Drinfeld module over $k$. We state and prove an equivariant refinement of Taelman's analogue of the analytic class number formula for $(E,K/k)$, and derive explicit conseq
Externí odkaz:
http://arxiv.org/abs/2309.17256
Let $A/\mathbb{Q}$ be a Jacobian variety and let $F$ be a totally real, tamely ramified, abelian number field. Given a character $\psi$ of $F/\mathbb{Q}$, Deligne's Period Conjecture asserts the algebraicity of the suitably normalised value $\mathcal
Externí odkaz:
http://arxiv.org/abs/2302.10044
We construct a canonical family of elements in the reduced exterior power lattices of the unit groups of global fields. We prove that this family recovers the theory of cyclotomic elements in real abelian fields and also establish detailed arithmetic
Externí odkaz:
http://arxiv.org/abs/2111.11109
Autor:
Bley, Werner, Castillo, Daniel Macias
Let $A$ be an abelian variety defined over a number field $k$, let $p$ be an odd prime number and let $F/k$ be a cyclic extension of $p$-power degree. Under not-too-stringent hypotheses we give an interpretation of the $p$-component of the relevant c
Externí odkaz:
http://arxiv.org/abs/1912.11260
We develop a theory of `non-abelian higher special elements' in the non-commutative exterior powers of the Galois cohomology of $p$-adic representations. We explore their relation to the theory of organising matrices and thus to the Galois module str
Externí odkaz:
http://arxiv.org/abs/1910.00569
Autor:
Burns, David, Castillo, Daniel Macias
We consider refined conjectures of Birch and Swinnerton-Dyer type for the Hasse-Weil-Artin L-series of abelian varieties over general number fields. We shall, in particular, formulate several new such conjectures and establish their precise relation
Externí odkaz:
http://arxiv.org/abs/1909.03959
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