General information | Course description | Homework assignments | Grading policies | Other texts | Links

**Lecture:** Tuesday and Thursday, 13:45 – 15:00, Physics Building 227

**Name:** Prof. Ezra Miller (you should call me "Ezra")
**Address:** Mathematics Department,
Duke University, Box 90320,
Durham, NC 27708-0320
**Office:** Physics 209
**Phone:** (919) 660-2846
**Email:** *ezramath.duke.edu*
**Webpage:**
*https://math.duke.edu/people/ezra-miller*
**Course webpage:** you're already looking at it...
but it's *http://math.duke.edu/~ezra/627/627.html*
**Office hours:** Tuesday and Thursday, 12:45 – 13:45, Physics 209

- sheaves
- spectrum of a ring
- schemes (affine, projective, neither)
- types of schemes (reduced, normal, factorial, regular)
- morphisms of schemes: immersions, finiteness conditions
- quasicoherent sheaves
- fiber products
- affine and projective morphisms
- separated and proper morphisms
- line bundles

- Tentative due dates for the homework assignments this semester are listed in the table below. You will have approximately two weeks to do each assignment.
**All solutions you turn in must be typewritten**using the LaTeX templates provided for each of the homework assignments. Communicating your ideas is an integral part of being a mathematician. It is essential that you learn this skill in graduate school. Simply fill your responses into the provided LaTeX files; the formatting and macros in the preamble are designed to enable grading, and altering those would disable their functionality. I will be happy to answer any questions you might have about LaTeX, although you should ask your classmates first.**Turn in your homework solutions by sending electronic versions to me**. Send your .tex file (I may comment on your LaTeX usage) and include your .pdf file as verification that your system produces the same thing as mine does.**Do not print your solutions.**This will save paper. I will not read or otherwise use the printed version anyway.**I encourage collaboration on homework**, but**Each student must write their own solutions using their own words**, and**Indicate—on the homework page—who your collaborators were**.**You must cite sources in your solutions.**If you rely on so-and-so's theorem, then you must state the theorem and tell me where you found it. Be specific: "the local-ringed spaces proposition" is not precise; in contrast, "[Vakil, Proposition 7.3.1]" is. (Even better would be, "a key result on morphisms of affine schemes as local-ringed spaces [Vakil, Proposition 7.3.1]".) Theorems can be known by many names or designations, so I'm likely not to recognize many theorems by names you might attach.**Late homework will not be accepted.**Early homework is fine.- Homework solutions should be thoroughly explained: there will be no credit for unsupported answers.

Assignment | Due Date | Problems |
---|---|---|

Homework #1 |
Tue. 13 September | in LaTeX or PDF |

Homework #2 |
Tue. 27 September | in LaTeX or PDF |

Homework #3 |
Thu. 13 October | in LaTeX or PDF |

Homework #4 |
Thu. 27 October | in LaTeX or PDF |

Homework #5 |
Thu. 10 November | in LaTeX or PDF |

Homework #6 |
Tue. 29 November | in LaTeX or PDF |

Level | Title | Author(s) | Publisher, date |
---|---|---|---|

Lower | Algebraic Geometry, a first course | Harris | Springer, 1995 |

Comparable | Algebraic Geometry | Hartshorne | Springer, 1977 |

Comparable | The Geometry of Schemes | Eisenbud & Harris | Springer, 2000 |

Comparable | Principles of Algebraic Geometry | Griffiths & Harris | Wiley, 1978 |

- list of all courses given in the Math Department in Fall 2022
- Official University calendar for academic year 2022–2023
- Duke Community Standard
- Fundamental University definitions and policies concerning academic dishonesty and related matters
- How student conduct issues are resolved

Many thanks are due to Jeremy Martin and Vic Reiner, who provided templates for this webpage long ago.

The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by Duke University.

*ezramath.duke.edu*

*Mon Aug 29 23:44:26 EDT 2022*

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