This seminar will normally take place on Wednesdays at 14.00 in room 116, starting 24th January. The aim is to go over the basics of affine and global schemes (and perhaps Grothendieck topologies).

One potential source is the recent Springer book by Siegfried Bosch, *Algebraic Geometry and Commutative Algebra* which can be downloaded via the library website. Another useful source is Eisenbud & Harris, *The Geometry of Schemes* although this only exists as a single library copy. However there are many other sources.

Here is a suggested breakdown of topics, I am happy to do the first few sessions but it would be nice if some other volunteers would offer to talk. The numbers in brackets are guesstimates of sessions required.

1) Presheaves and sheaves: quick introduction. Locally ringed spaces. (2)

2) Affine schemes. (2)

3) Global schemes. Constructions such as pullbacks. (1-2)

4) Coherent sheaves and cohomological ideas (1-2)

5) Grothendieck topologies and sites. (1-2)

**Some reading material **

Siegfried Bosch, *Algebraic Geometry and Commutative Algebra*

http://www.maths.gla.ac.uk/~ajb/Schemes/Bosch-AlgGeomCommAlg.pdf

Eisenbud & Harris, *The Geometry of Schemes*

http://www.maths.ed.ac.uk/~aar/papers/eisenbudharris.pdf

*A rough guide to Schemes* (updated 19/02/2018, now contains material

on prime spectra and affine schemes including some new examples, as

well as the beginnings of global schemes).

http://www.maths.gla.ac.uk/~ajb/Schemes/Schemes.pdf
**Note:** I have modified the paragraph on page 11 about embeddings -

Greg is right and this really needs doing properly with a discussion of

immersions and subschemes whch will come later.