Synthetic algebraic geometry is the study of algebraic geometry by synthetic means – instead of building up everything from ZF(C), we reason internally to a topos which contains the objects of interest. This topos is called the higher Zariski topos and is given by higher Zariski-sheaves on affine schemes of finite type over an arbitrary base ring. Higher sheaves are neccessary to interpret homotopy type theory. This provides us with an easy access to cohomology groups.
If you like to know more about synthetic algebraic geometry you can check out this hottest-talk, the website of the last meeting or you can go directly to the youtube-playlist of this meeting. An overview of the results and subtopics of synthetic algebraic geometry is on github.
Contact us if you would like to join the workshop!
All the best,
Felix Cherubini and Hugo Moeneclaey