On refined conjectures of Birch and Swinnerton-Dyer type for Hasse-Weil-Artin L-series / David Burns, Daniel Macias Castillo.

By:

Burns, David, 1963- [author.]

Contributor(s):

Castillo, Daniel Macias [author.]

Material type: Text

text

Media type:

unmediated

Carrier type:

volume

ISBN:

1470469669
9781470469665

Subject(s):

DDC classification:

B967o

Abstract: We consider refined conjectures of Birch and Swinnterdon-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 to previous conjectures, including to the relevant special case of the equivariant Tamagawa number conjecture. We also derive a wide range of concrete interpretations and explicit consequences of these conjectures that, in general, involve a thoroughgoing mixture of difficult Archimedean considerations related to refinements of the conjecture of Deligne and Gross and delicate p-adic congruence relations that involve the bi-extension height pairing of Mazur and Tate and are related to key aspects of noncommutative Iwasawa theory. In important special cases we provide strong evidence, both theoretical and numerical, in support of the conjectures.

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Holdings
Item type	Current library	Collection	Call number	Status	Date due	Barcode
Books	Castorina	Coleções de Monografias (Monographs Collections)		Available		39063000809598

"May 2024 ; volume 297 ; number 1482 (first of 5 numbers)."

Includes bibliographical references (pages 151-156).

We consider refined conjectures of Birch and Swinnterdon-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 to previous conjectures, including to the relevant special case of the equivariant Tamagawa number conjecture. We also derive a wide range of concrete interpretations and explicit consequences of these conjectures that, in general, involve a thoroughgoing mixture of difficult Archimedean considerations related to refinements of the conjecture of Deligne and Gross and delicate p-adic congruence relations that involve the bi-extension height pairing of Mazur and Tate and are related to key aspects of noncommutative Iwasawa theory. In important special cases we provide strong evidence, both theoretical and numerical, in support of the conjectures.

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