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Algebraic varieties
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301	Elliptic curves, their companions, and their statistics Barry Mazur What is the probability that a cubic plane curve with rational coefficients has infinitely many rational points? Questions of this type (more exactly fo Add to Reading List Source URL: www.math.harvard.edu Language: English - Date: 2011-12-13 10:36:46 Diophantine geometry Elliptic curves Abelian varieties Analytic number theory Group theory Mordell–Weil theorem Rational point Arithmetic of abelian varieties Curve Abstract algebra Mathematics Algebraic geometry
302	Ideals, Varieties and Macaulay 2 Bernd Sturmfels? This chapter introduces Macaulay 2 commands for some elementary computations in algebraic geometry. Familiarity with Gr¨ obner bases is assumed. Many students and resear Add to Reading List Source URL: www.math.uiuc.edu Language: English - Date: 2001-04-28 11:06:43 Commutative algebra Polynomials Algebraic structures Algebraic geometry Monomial order Ideal Monomial Polynomial ring Polynomial Abstract algebra Algebra Ring theory
303	Needles in a Haystack: Special Varieties via Small Fields Frank-Olaf Schreyer and Fabio Tonoli In this article we illustrate how picking points over a finite field at random can help to investigate algebraic geometry que Add to Reading List Source URL: www.math.uiuc.edu Language: English - Date: 2001-04-28 11:04:05 Algebraic curves Moduli theory Vector bundles Algebraic varieties Moduli space Canonical bundle Special divisor Curve Hilbert scheme Algebraic geometry Geometry Abstract algebra
304	A Geometric View of Cryptographic Equation Solving S. Murphy and M.B. Paterson? Information Security Group Royal Holloway University of London Add to Reading List Source URL: www.isg.rhul.ac.uk Language: English - Date: 2007-12-13 09:42:56 Projective geometry Algebraic varieties Tensors Algebraic geometry Multilinear algebra Veronese surface Projective space Homogeneous polynomial Collineation Algebra Geometry Mathematics
305	A Geometric View of Cryptographic Equation Solving Sean Murphy and Maura Paterson Technical Report RHUL–MA–2007–4 Add to Reading List Source URL: www.ma.rhul.ac.uk Language: English - Date: 2007-05-18 08:53:52 Projective geometry Algebraic varieties Tensors Multilinear algebra Algebraic geometry Veronese surface Projective space Homogeneous polynomial Symmetric tensor Algebra Geometry Mathematics
306	William A. Stein[removed]Curriculum Vitae – April 2013 · Add to Reading List Source URL: sage.math.washington.edu Language: English - Date: 2013-04-04 22:09:51 Number theory Diophantine geometry Elliptic curves Analytic number theory Abelian varieties Tate–Shafarevich group Birch and Swinnerton-Dyer conjecture Heegner point Peter Swinnerton-Dyer Mathematics Abstract algebra Algebraic geometry
307	William A. Stein[removed]Curriculum Vitae – April 2013 · Add to Reading List Source URL: wstein.org Language: English - Date: 2013-04-04 22:09:51 Number theory Diophantine geometry Elliptic curves Analytic number theory Abelian varieties Tate–Shafarevich group Birch and Swinnerton-Dyer conjecture Heegner point Peter Swinnerton-Dyer Mathematics Abstract algebra Algebraic geometry
308	Projective Geometry and Homological Algebra David Eisenbud? We provide an introduction to many of the homological commands in Macaulay 2 (modules, free resolutions, Ext and Tor[removed]by means of examples showing how to Add to Reading List Source URL: www.math.uiuc.edu Language: English - Date: 2001-04-28 11:05:10 Multilinear algebra Algebraic varieties Interpolation Algebraic geometry Homogeneous polynomial Jacobian matrix and determinant Proj construction Homogeneous coordinate ring Cluster algebra Algebra Mathematics Linear algebra
309	D-modules and Cohomology of Varieties Uli Walther In this chapter we introduce the reader to some ideas from the world of differential operators. We show how to use these concepts in conjunction with Macaulay 2 to obtain Add to Reading List Source URL: www.math.uiuc.edu Language: English - Date: 2001-04-28 11:04:26 Commutative algebra Ring theory Module theory Algebraic structures D-module Local cohomology Sheaf Finitely-generated module Local ring Abstract algebra Algebra Homological algebra
310	Some comments on elliptic curves over general number fields and Brill-Noether modular varieties B. Mazur November 3, 2013 Very rough notes for a lecture to be given October 5, 2013 at the Quebec/Maine Number Theory Add to Reading List Source URL: www.math.harvard.edu Language: English - Date: 2013-11-03 12:11:28 Elliptic curves Algebraic curves Analytic number theory Group theory Diophantine geometry Modular curve Canonical bundle Torsion tensor Mordell–Weil theorem Abstract algebra Geometry Mathematics

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