1. Description:

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. Outline:

We will mainly cover standard contents on schemes, equivalently, Chapter II Sections 1-7 of Hartshorne’s textbook [1]: Sheaves and pressheaves, locally ringed spaces, schemes, separated and proper morphisms, quasi-coherent and coherent sheaves, Weil and Carlier divisors, projective morphisms. 

 

References: 

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

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

[3] D. Harari, Schemes, Tsinghua Lecture Notes, 2005. 

 

Registration:

https://forms.gle/1PXFY9EGYUsXtKVc9