Algebraic Geometry - MA745 - Spring 2015 |

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Course: MA745, Algebraic Geometry

Professor: Jared Weinstein

Lecture: MWF 2-3, MCS B23

This course is an introduction to modern algebraic geometry. Topics include category theory, sheaves, the definition of a scheme, curves, the Riemann-Roch theorem, and perhaps a few other topics, time permitting.

The Rising Sea: Foundations of Algebraic Geometry, by Ravi Vakil.

Exercises are so essential for learning this material that I am making them worth 100% of the course grade. They will be due each Friday. I won't be grading them in detail, but I do reserve the right to ask you to redo them if they are inadequate.

HW | Assignment | Due |
---|---|---|

#1 | 1.2A,B; 1.3A, B, C, D, H, N, O. | Jan. 30 |

#2 | 1.3T, U; 14.B, F; 2.2A, B, C, J. | Feb. 6 |

#3 | 3.1A, B; 3.2C, E, G, H, K. | Feb. 13 |

#4 | 3.4C(c), D, F; 3.5A, E, 3.6E. Also: show that Spec A is disconnected if and only if A is a product of two nonzero rings. | Feb. 20 |

#5 | 3.7C, D, E; 4.1A, D; 4.3A, B. | Feb. 27 |

#6 | 4.5E, F; 5.1A; 5.2A, B, C. | Mar. 6 |

#7 | 5.3C, E; 5.4A, F; 6.2A, E; 6.3C, D. | Mar. 20 |

#8 | 6.3N; 6.4C; 6.5A, B, G, H, J. | Mar. 27 |

#9 | 7.2A, F(a), H; 7.3H, K, M. | Apr. 3 |

#10 | 12.1G, H, I; 12.2A, D, J. | Apr. 10 |

#11 | 13.1B, G; 14.1B, C, D; 14.2 E, O. | Apr. 24 |

#12 | 194A; 19.9A, B, C, D, F. | (optional) |