Author: Theodore HwaPublisher:
ISBN:
Category :
Languages : en
Pages : 70
Book Description
Galois Representations Associated to Torsion Points of Elliptic Curves
Author: Theodore HwaGalois Representations Associated to Torsion Points of Elliptic Curves
Author: Seong Eun JungPublisher:
ISBN:
Category : Curves, Elliptic
Languages : en
Pages : 46
Book Description
Galois representations from non-torsion points on elliptic curves
Author: Matthew HughesPublisher:
ISBN:
Category : Algebraic number theory
Languages : en
Pages : 0
Book Description
Mod 4 Galois Representations and Elliptic Curves
Author: Christopher HoldenRational Points on Elliptic Curves
Author: Joseph H. SilvermanPublisher: Springer Science & Business Media
ISBN: 1475742525
Category : Mathematics
Languages : en
Pages : 292
Book Description
The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, providing an opportunity for readers to appreciate the unity of modern mathematics. The book’s accessibility, the informal writing style, and a wealth of exercises make it an ideal introduction for those interested in learning about Diophantine equations and arithmetic geometry.
Abelian l-Adic Representations and Elliptic Curves
Author: Jean-Pierre SerrePublisher: CRC Press
ISBN: 1439863865
Category : Mathematics
Languages : en
Pages : 203
Book Description
This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one
Rational Points on Elliptic Curves
Author: Joseph H. SilvermanPublisher: Springer
ISBN: 3319185888
Category : Mathematics
Languages : en
Pages : 349
Book Description
The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This volume stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make Rational Points on Elliptic Curves an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry. Most concretely, an elliptic curve is the set of zeroes of a cubic polynomial in two variables. If the polynomial has rational coefficients, then one can ask for a description of those zeroes whose coordinates are either integers or rational numbers. It is this number theoretic question that is the main subject of Rational Points on Elliptic Curves. Topics covered include the geometry and group structure of elliptic curves, the Nagell–Lutz theorem describing points of finite order, the Mordell–Weil theorem on the finite generation of the group of rational points, the Thue–Siegel theorem on the finiteness of the set of integer points, theorems on counting points with coordinates in finite fields, Lenstra's elliptic curve factorization algorithm, and a discussion of complex multiplication and the Galois representations associated to torsion points. Additional topics new to the second edition include an introduction to elliptic curve cryptography and a brief discussion of the stunning proof of Fermat's Last Theorem by Wiles et al. via the use of elliptic curves.
Elliptic Curves Over Finite Fields and Their L-Torsion Galois Representations
Author: Michael BakerPublisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Let $q$ and $\ell$ be distinct primes. Given an elliptic curve $E$ over $\mathbf{F}_q$, we study the behaviour of the 2-dimensional Galois representation of $\mathrm{Gal}(\overline{\mathbf{F}_q}/\mathbf{F}_q) \cong \widehat{\mathbf Z}$ on its $\ell$-torsion subgroup $E[\ell]$. This leads us to the problem of counting elliptic curves with prescribed $\ell$-torsion Galois representations, which we answer for small primes $\ell$ by counting rational points on suitable modular curves. The resulting exact formulas yield expressions for certain sums of Hurwitz class numbers.
Icosahedral Galois Representations and Elliptic Curves
Author: Annette KluteElliptic Curves and Big Galois Representations
Author: Daniel DelbourgoPublisher: Cambridge University Press
ISBN: 0521728665
Category : Mathematics
Languages : en
Pages : 283
Book Description
Describes the arithmetic of modular forms and elliptic curves; self-contained and ideal for both graduate students and professional number theorists.