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Hu, Yan (2019) Rationality of Darmon Points Over Genus Fields of Nonmaximal Orders. [Ph.D. thesis]

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Abstract (italian or english)

Stark-Heegner points, also known as Darmon points, were introduced by H. Darmon in [11], as certain local points on rational elliptic curves, conjecturally defined over abelian extensions of real quadratic fields. The rationality conjecture for these points is only known in the unramified case, namely, when these points are specializations of global points defined over the strict Hilbert class field H+ F of the real quadratic field F and twisted by (unramified) quadratic characters of Gal(H+ F /F). We extend these results to the situation of ramified quadratic characters; we show that Darmon points of conductor c ≥ 1 twisted by quadratic characters of G+ c =Gal(H+ c /F), where H+ c is the strict ring class field of F of conductor c, come from rational points on the elliptic curve defined over H+ c.

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EPrint type:Ph.D. thesis
Tutor:Longo, Matteo
Ph.D. course:Ciclo 31 > Corsi 31 > SCIENZE MATEMATICHE
Data di deposito della tesi:13 February 2019
Anno di Pubblicazione:13 February 2019
Key Words:number theory, Darmon points, modular form
Settori scientifico-disciplinari MIUR:Area 01 - Scienze matematiche e informatiche > MAT/03 Geometria
Struttura di riferimento:Dipartimenti > Dipartimento di Matematica
Codice ID:11787
Depositato il:06 Nov 2019 11:14
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