1. Course Background & Purposes

Schemes are most fundamental objects in Algebraic Geometry and is an important language used Number Theory and Arithmetic Geometry, particularly of describing families of varieties in modern theory.  The goal of this this short course is to bring in another occasion for investigating schemes together, particularly for students those do not have the chance to encounter it or wish to have a second chance to revisit them.

2. Course Outline & Descriptions

We will mainly cover standard contents on schemes, equivalently, Chapter II Sections 1-7 of Hartshorne’s textbook [1]: Sheaves and presheaves, locally ringed spaces, schemes, separated and proper morphisms, quasi-coherent and coherent sheaves, Weil and Carlier divisors, projective morphisms. We plan to go over Sections 1-4 in less details and cover Sections 5-7 in more details.

References:

[1] R. Hartshorne Algebraic Geometry GTM 52, 1977.

[2] D. Mumford, The Red Book of Varieties and Schemes, LNM 1358, 1999.

3. Grading

There is no grading and no credits offered in this short course.

Registration