Thursday, July 28, 2016

Modular Function of Weight k > 2: The Eisenstein Series

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MathJax TeX Test Page Let $k > 2$ be an integer, and consider the following function defined on the upper half plane of the comple...
Saturday, July 23, 2016

Galois Correspondence of Deck Transformations (5.2)

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MathJax TeX Test Page Let $p : Y → X$ be the universal covering, with $\text{Deck}(Y/X)$ its set of deck transformations. If $G ≤ \te...
Monday, June 27, 2016

Algebraic Properties of Character Values (18.3.11-12,14,16-24)

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Dummit and Foote Abstract Algebra , section 18, exercises 11, 12, 14-24: MathJax TeX Test Page Let $G$ be a finite group of order $...
Sunday, May 8, 2016

Reorganization of Chapter 4.3

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William Fulton Algebraic Curves , chapter 4, section 3 MathJax TeX Test Page Throughout, let $φ=φ_{n+1}$, and let $τ : k[x_1,...,x_...
Friday, April 29, 2016

Plane Curve Multiplicities Under Polynomial Mappings (3.1.8)

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William Fulton Algebraic Curves , chapter 3, section 1, exercise 8: MathJax TeX Test Page Let $k$ be an algebraically closed field,...
Wednesday, April 27, 2016

Finite Dimensional Rings Containing Algebraically Closed Fields (2.9.47)

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William Fulton Algebraic Curves , chapter 2, section 9, exercise 47: MathJax TeX Test Page Let $R$ be a commutative ring sharing an...
Saturday, April 23, 2016

Multiple Representations are Required to Identify the Pole Set of a Rational Function (2.4.20)

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William Fulton Algebraic Curves , chapter 2, section 4, exercise 20: MathJax TeX Test Page Let $k$ be algebraically closed, and con...