Places,valuation rings and discrete valuations of a function field; the rational function field; divisors, Weil different adeles, genus; Riemann-Roch Theorem and its consequences; extensions of function fields, ramification, Hurwitz genus formula; constant field extensions, Galois extensions, Kummer and Artin-Schreier extensions.
Algebraic Function Fields (MATH 636)
2022 Fall
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
10
Nurdagül Anbar Meidl nanbar@sabanciuniv.edu,
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English
Doctoral, Master
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Programs\Type | Required | Core Elective | Area Elective |
Computer Science and Engineering - With Bachelor's Degree | * | ||
Computer Science and Engineering - With Master's Degree | * | ||
Computer Science and Engineering - With Thesis | * | ||
Cyber Security - With Bachelor's Degree | * | ||
Cyber Security - With Master's Degree | * | ||
Cyber Security - With Thesis | * | ||
Data Science - With Thesis | * | ||
Electronics Engineering and Computer Science - With Bachelor's Degree | * | ||
Electronics Engineering and Computer Science - With Master's Degree | * | ||
Electronics Engineering and Computer Science - With Thesis | * | ||
Electronics Engineering - With Bachelor's Degree | * | ||
Electronics Engineering - With Master's Degree | * | ||
Electronics Engineering - With Thesis | * | ||
Energy Technologies and Management-With Thesis | * | ||
Industrial Engineering - With Bachelor's Degree | * | ||
Industrial Engineering - With Master's Degree | * | ||
Industrial Engineering - With Thesis | * | ||
Leaders for Industry Biological Sciences and Bioengineering - Non Thesis | * | ||
Leaders for Industry Computer Science and Engineering - Non Thesis | * | ||
Leaders for Industry Electronics Engineering and Computer Science - Non Thesis | * | ||
Leaders for Industry Electronics Engineering - Non Thesis | * | ||
Leaders for Industry Industrial Engineering - Non Thesis | * | ||
Leaders for Industry Materials Science and Engineering - Non Thesis | * | ||
Leaders for Industry Mechatronics Engineering - Non Thesis | * | ||
Manufacturing Engineering - Non Thesis | * | ||
Manufacturing Engineering - With Bachelor's Degree | * | ||
Manufacturing Engineering - With Master's Degree | * | ||
Manufacturing Engineering - With Thesis | * | ||
Materials Science and Nano Engineering-(Pre:Materials Science and Engineering) | * | ||
Materials Science and Nano Engineering-(Pre:Materials Science and Engineering) | * | ||
Materials Science and Nano Engineering - With Thesis (Pre.Name: Materials Science and Engineering) | * | ||
Mathematics - With Bachelor's Degree | * | ||
Mathematics - With Master's Degree | * | ||
Mathematics - With Thesis | * | ||
Mechatronics Engineering - With Bachelor's Degree | * | ||
Mechatronics Engineering - With Master's Degree | * | ||
Mechatronics Engineering - With Thesis | * | ||
Molecular Biology, Genetics and Bioengineering (Prev. Name: Biological Sciences and Bioengineering) | * | ||
Molecular Biology, Genetics and Bioengineering-(Prev. Name: Biological Sciences and Bioengineering) | * | ||
Molecular Biology,Genetics and Bioengineering-With Thesis (Pre.Name:Biological Sciences and Bioeng.) | * | ||
Physics - Non Thesis | * | ||
Physics - With Bachelor's Degree | * | ||
Physics - With Master's Degree | * | ||
Physics - With Thesis | * |
CONTENT
LEARNING OUTCOMES
- - discuss the basic notions of the theory, like places, divisors, Riemann-Roch spaces, and genus of a function field.
- - recall the main results, centered around the Riemann-Roch theorem.
- - recall the notions of ramification and splitting in extensions of function fields.
- - apply these concepts in specific cases, in particular fields of small genus.
Update Date:
ASSESSMENT METHODS and CRITERIA
Percentage (%) | |
Final | 30 |
Midterm | 30 |
Individual Project | 40 |
RECOMENDED or REQUIRED READINGS
Textbook |
Algebraic Function Fields and Codes, by Henning Stichtenoth, 2nd Edition, Springer-Verlag, 2009. Graduate Texts in Mathematics No. 254. |