Congruences for critical values of higher derivatives of twisted Hasse-Weil L-functions, III

Bley, Werner und Macias Castillo, Daniel (2022): Congruences for critical values of higher derivatives of twisted Hasse-Weil L-functions, III. In: Mathematical Proceedings of the Cambridge Philosophical Society, Bd. 173, Nr. 2: S. 431-456

Abstract

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 case of the equivariant Tamagawa number conjecture in terms of integral congruence relations involving the evaluation on appropriate points of A of the Gal(F/k)-valued height pairing of Mazur and Tate. We then discuss the numerical computation of this pairing, and in particular obtain the first numerical verifications of this conjecture in situations in which the p-completion of the Mordell-Weil group of A over F is not a projective Galois module.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Informatik
• Themengebiete: 000 Informatik, Informationswissenschaft, allgemeine Werke > 004 Informatik
• ISSN: 0305-0041
• Sprache: Englisch