On the symplectic type of isomorphisms of the p-torsion of elliptic curves

On the symplectic type of isomorphisms of the p-torsion of elliptic curves

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Détails bibliographiques
Auteurs principaux : Freitas Nuno (Auteur), Kraus Alain (Auteur)
Format : Livre
Langue : anglais
Titre complet : On the symplectic type of isomorphisms of the p-torsion of elliptic curves / Nuno Freitas, Alain Kraus
Publié : Providence (R.I.) : American Mathematical Society , 2022
Description matérielle : 1 vol. (V-105 p.)
Collection : Memoirs of the American Mathematical Society ; 1361
Sujets :
Isomorphismes (mathématiques)
Courbes elliptiques
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200 1 |a On the symplectic type of isomorphisms of the p-torsion of elliptic curves  |f Nuno Freitas, Alain Kraus 
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225 2 |a Memoirs of the American Mathematical Society  |x 0065-9266  |v Number 1361 
300 |a "May 2022, volume 277, number 1361 (first of 6 numbers)." 
320 |a Bibliogr. p. 103-105 
359 2 |b Chapter 1. Motivation and results  |c 1.1 Introduction  |c 1.2 A double motivation  |c 1.3 Our approach to the problem of determining the symplectic type  |c 1.4 A complete list of local symplectic criteria at l<>p  |b Chapter 2. The existence of local symplectic criteria  |c 2.1 Existence of symplectic criteria in terms of the image of PE,p  |c 2.2 Symplectic criteria with PE,p (GQe) abelian  |b Chapter 3. The criterion in the case of good reduction  |c 3.1 The action of Frobenius  |c 3.2 Proof of Theorem 1.18  |c 3.3 A more general theorem  |b Chapter 4. Elliptic curves with potentially good reduction  |c 4.1 An useful Weierstrass model  |c 4.2 The field of good reduction  |c 4.3 The Galois group of the p-torsion field in the cases e=3, 4  |c 4.4 Proof of Theorem 1.4  |c 4.5 Proof of Lemmas 1.7, 1.8, 1.16 and 1.17  |c 4.6 The completeness of Table 1.1  |b Chapter 5. The morphism YE  |c 5.1 Explicit description of YE  |c 5.2 The morphism of YE in the tame case e=3  |c 5.3 The morphism YE in the wild case e=3  |c 5.4 The morphism YE in the tame case e=4  |c 5.5 The morphism YE in the wild case e=4  |c 5.6 The morphism YE in the wild case e=8  |c 5.7 The morphism in the wild case e=12  |c 5.8 Tables with coordinate changes  |b Chapter 6. Proof of the criteria  |c 6.1 Proof of Theorem 1.3  |c 6.2 Proof of Theorem 1.5  |c 6.3 Proof of Theorem 1.6  |c 6.4 Proof of Theorem 1.9  |c 6.5 proof of Theorem 1.10  |c 6.6 Proof of Theorem 1.22  |c 6.7 Proof of Theorems 1.13 and 1.15  |b Chapter 7. Applications  |c 7.1 Revisiting a question of Mazur  |c 7.2 The Generalized Fermat equation x2 + y3 = zp  |c 7.3 On the hyperelliptic curves y2 = xp - l and y2 = xp - 2l  |b Bibliography 
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