✦ LIBER ✦

Supersingular Abelian Varieties over Finite Fields

✍ Scribed by Hui June Zhu

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 181 KB
Volume: 86
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.2000.2562

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

Group Structures of Elementary Supersing

Group Structures of Elementary Supersingular Abelian Varieties over Finite Fields

✍ Hui June Zhu 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 176 KB

Let A be a supersingular abelian variety over a finite field k which is k-isogenous to a power of a simple abelian variety over k. Write the characteristic polynomial of the Frobenius endomorphism of A relative to k as f = g e for a monic irreducible polynomial g and a positive integer e. We show th

On Supersingular Abelian Varieties of Di

On Supersingular Abelian Varieties of Dimension Two over Finite Fields

✍ Chaoping Xing 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 243 KB

In this paper we study the characteristic polynomials and the rational point group structure of supersingular varieties of dimension two over finite fields. Meanwhile, we also list all L-functions of supersingular curves of genus two over ‫ކ‬ 2 and determine the group structure of their divisor clas

Isogeny Classes of Hilbert–Blumenthal Ab

Isogeny Classes of Hilbert–Blumenthal Abelian Varieties over Finite Fields

✍ Jeffrey D. Achter; Clifton L.R. Cunningham 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 244 KB

This paper was written at the University of Massachusetts at Amherst. We thank the working seminar on Shimura varieties there for patiently listening to us as we worked through these results. Our thanks also go to R. Schoof for his encouragement and suggestions, as well as to our anonymous (but inva

Counting Points on Curves and Abelian Va

Counting Points on Curves and Abelian Varieties Over Finite Fields

✍ Leonard M. Adleman; Ming-Deh Huang 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 343 KB

We develop efficient methods for deterministic computations with semi-algebraic sets and apply them to the problem of counting points on curves and Abelian varieties over finite fields. For Abelian varieties of dimension g in projective N space over Fq, we improve Pila's result and show that the pro

Universal Norms on Abelian Varieties ove

Universal Norms on Abelian Varieties over Global Function Fields

✍ Matthew A. Papanikolas 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 169 KB

We examine the Mazur-Tate canonical height pairing defined between an abelian variety over a global field and its dual. We show in the case of global function fields that certain of these pairings are annihilated by universal norms coming from Carlitz cyclotomic extensions. Furthermore, for elliptic

Rational Points On Certain Abelian Varie

Rational Points On Certain Abelian Varieties Over Function Fields

✍ F. Hazama 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 269 KB

A structure theorem on the Mordell-Weil group of abelian varieties which arise as the twists associated with various double covers of varieties is proved. As an application, a three-parameter family of elliptic curves whose generic Mordell-Weil rank is four is constructed. * 1995 Academic Press. Inc