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Lectures on Numerical Methods in Bifurcation Problems
Methods for Finding Zeros in Polynomials
Lectures on Stochastic Flows and Applications
Educational Psychology by Edward L. Thorndike
The Last Days of Tolstoy by V. G. Chertkov
Globalization and Responsibility
Lectures on Siegel Modular Forms and Representation by Quadratic Forms
Lectures on Topics In One-Parameter Bifurcation Problems
History of the Incas by Pedro Sarmiento de Gamboa
Linear Algebra: Theorems and Applications
Lectures on Stochastic Differential Equations and Malliavin Calculus
A Short Biographical Dictionary of English Literature
Lectures on Sieve Methods and Prime Number Theory
Dollars and Sense by William Crosbie Hunter
The Theory of the Theatre by Clayton Hamilton
The Mathematics of Investment
Occupiers of Wall Street: Losers or Game Changers
The Solution of the Pyramid Problem
Lectures on Moduli of Curves
Walden by Henry David Thoreau
Methods for Finding Zeros in Polynomials
Lectures on Stochastic Flows and Applications
Educational Psychology by Edward L. Thorndike
The Last Days of Tolstoy by V. G. Chertkov
Globalization and Responsibility
Lectures on Siegel Modular Forms and Representation by Quadratic Forms
Lectures on Topics In One-Parameter Bifurcation Problems
History of the Incas by Pedro Sarmiento de Gamboa
Linear Algebra: Theorems and Applications
Lectures on Stochastic Differential Equations and Malliavin Calculus
A Short Biographical Dictionary of English Literature
Lectures on Sieve Methods and Prime Number Theory
Dollars and Sense by William Crosbie Hunter
The Theory of the Theatre by Clayton Hamilton
The Mathematics of Investment
Occupiers of Wall Street: Losers or Game Changers
The Solution of the Pyramid Problem
Lectures on Moduli of Curves
Walden by Henry David Thoreau
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Arithmetic Moduli of Elliptic Curves. (AM-108) (Annals of Mathematics Studies): Nicholas M. Katz, Barry Mazur
Posted on 2010-03-16
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More This book is devoted to giving an account of the arithmetic theory of the moduli spaces of elliptic curves. The main emphasis is on understanding the behavior of these moduli spaces at primes dividing the "level" of the moduli problem being considered. Until recently, this seemed a very difficult problem, because one had no apriori construction of these spaces at the "bad" primes. One defined them as schemes over, say, Z[1/N] as the solution to some well-posed moduli problem which only made sense for elliptic curves over rings in which N was invertible, and then one used a process of normalization to extend them to schemes over Z, e.g., one took the "proj" of the graded subring of the ring of all modular forms of the type in question consisting of those with intgeral Fourier ("q-expansion") coefficients at the cusps. This procedure produced a scheme over Z, but one had no idea of what meduli interpretation this scheme had, nor afortiori did one have any idea of the modular interpretation of its reduction modulo p, for p a prime dividing the level. Download Link (Uploading.com) To see my other books, click Download Link (Here).
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