Syllabus - FUNDAMENTAL CONCEPTS IN COMMUTATIVE ALGEBRA AND ALGEBRAIC GEOMETRY (80599)

Syllabus FUNDAMENTAL CONCEPTS IN COMMUTATIVE ALGEBRA AND ALGEBRAIC GEOMETRY - 80599
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Last update 24-01-2024
HU Credits: 6 Degree/Cycle: 2nd degree (Master) Responsible Department: Mathematics Semester: 1st Semester Teaching Languages: English and Hebrew Campus: E. Safra Course/Module Coordinator: Prof. Michael Termkin Coordinator Email: michael.temkin@mail.huji.ac.il Coordinator Office Hours: By appointment Teaching Staff: Prof Michael Temkin, Mr. Omri Solan Course/Module description: The main topics of the course are 1) The basic theory of commutative unital rings and their modules. 2) A very basic theory of algebraic varieties. Course/Module aims: Introduction to commutative algebra and algebraic geometry Learning outcomes - On successful completion of this module, students should be able to: Familiarity with basic concepts in commutative algebra and algebraic geometry. Building the foundations for further research in this field. Attendance requirements(%): 0 Teaching arrangement and method of instruction: Lecture+Exercise Course/Module Content: Unital commutative rings, ideals, modules, localizations, prime ideals and the topological space Spec(A). Modules, lemma of Nakayama, tensor product, exactness. Integral extensions, Noether normalization and Hilbert Nullstellensatz theorems. Noetherian rings and modules, Hilbert basis theorem Affine and projective varieties over an algebraically closed field, regular and rational functions, spaces of functions and abstract algebraic varieties, dimension theory, algebraic groups, Bezout theorem. Required Reading: The course will come with lecture notes Additional Reading Material: "Introduction to commutative algebra" by Atiyah and Macdonald, Ch 1-3,5,7 "Algebraic varieties" by Kempf, Ch 1-3. "Algebraic geometry" by Hartshorne, Ch 1. "The Red Book of Varieties and Schemes", by D. Mumford, Ch. 1 Grading Scheme : Written / Oral / Practical Exam 50 % Submission assignments during the semester: Exercises / Essays / Audits / Reports / Forum / Simulation / others 50 % Additional information: In case it will not be possible to give an ordinary exam, 50% of the grade will be determined by a home assignment, which will replace the exam.

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