Since the last update of October 2014 we have added the following material:

- Structure modules over PIDs following Warfield Tag 0ASL
- Correct proof of Lemma Tag 05U9 thanks to Ofer Gabber
- A flat ring map which is not a directed colimit of flat finitely presented ring maps Tag 0ATE
- Glueing dualizing complexes Tag 0AU5
- Trace maps Tag 0AWG
- Duality for a finite morphism Tag 0AWZ
- Grauert-Riemenschneider for surfaces Tag 0AX7
- Torsion free modules Tag 0AVQ
- Reflexive modules Tag 0AVT
- Finiteness theorem for f_* Tag 0AW7
- Fix definition of depth (thanks to Burt) Tag 00LE and Tag 0AVY
- Characterizing universally catenary rings Tag 0AW1
- Improved section on Jacobson spaces thanks to Juan Pablo Acosta Lopez Tag 005T
- Faithfully flat descent of ML modules thanks to Juan Pablo Acosta Lopez Tag 05A5
- Improvements to the chapter on Chow homology discussed here
- Degrees of vector bundles on curves Tag 0AYQ
- Degrees of zero cycles Tag 0AZ0 and how this relates to degrees of vector bundles and with numerical intersections
- Quotient by category of torsion modules thanks to Ingo Blchschmidt Tag 0B0J
- New chapter on intersection theory discussed here
- Example of different colimit topologies Tag 0B2Y
- Section on topological groups, rings, modules Tag 0B1Y
- Section on tangent spaces Tag 0B28
- A bunch of material on (quasi-)projectivity, for example Tag 0B41 and Tag 0B44
- Glueing in a modification Tag 0B3W at a point of a scheme
- Improved material on sober spaces thanks to Fred Rohrer Tag 004U
- Riemann-Roch and duality for curves Tag 0B5B
- Fix idiotic mistake about graded projective modules, thanks to Rishi Vyas read his explanation on github
- Base change map in duality Tag 0AA5 is often an isomorphism (Tag 0AA8) and commutes with base change Tag 0AWG
- Bunch of changes thanks to Darij Grinberg
- Material on group schemes over fields Tag 047J
- Material on (locally) algebraic group schemes over fields Tag 0BF6
- Thickenings of quasi-affine schemes are quasi-affine Tag 0B7L
- Minimal closed subspaces which aren’t schemes Tag 0B7X
- Monomorphisms of algebraic spaces Tag 0B89
- Change of base field and schematic locus Tag 0B82
- Separated group algebraic spaces over fields are schemes Tag 0B8G
- Picard scheme of smooth projective curves over algebraically closed fields Tag 0B92
- Improved discussion of invertible modules… (too ashamed to put a link here)
- Jacobson algebraic spaces Tag 0BA2
- Nagata spaces Tag 0BAT
- For an algebraic space: locally Noetherian + decent => quasi-separated Tag 0BB6
- Various improvements on rational and birational maps Tag 01RR, Tag 01RN, and Tag 0BAJ
- Dimension formula for algebraic spaces Tag 0BAW
- Generically finite morphisms of algebraic spaces Tag 0BBA
- Birational morphisms of algebraic spaces Tag 0ACU
- Elementary etale neighbourhoods on algebraic spaces Tag 03IG
- Complements of affine opens have codimension 1 Tag 0BCQ
- Norms of invertible modules Tag 0BCX which allows us to descend ample invertible modules
- Descending (quasi-)projectivity through field extensions Tag 0BDB
- Section on splitting complexes Tag 0BCF for better handling of local structure of perfect complexes
- Section on stably free modules Tag 0BC2
- Jumping loci for perfect complexes on schemes Tag 0BDH
- Applications of cohomology and base change Tag 0BDM
- Theorem of the cube Tag 0BEZ
- Weil divisors on locally Noetherian schemes Tag 0BE0
- The Weil divisor class associated to an invertible module Tag 02SE
- K\”unneth formula for schemes over a field Tag 0BEC
- Algebraic group schemes are quasi-projective Tag 0BF7
- Numerical intersections Tag 0BEL
- Section on abelian varieties Tag 0BF9 containing just enough for our use later
- Tried to improve the exposition of convergence for spectral sequences using terminology mostly as in Weibel; still very far from perfect
- Long overdue characterization of algebraic spaces Tag 0BGQ
- Chapters on resolution of surface singularities one for schemes and one for algebraic spaces

Enjoy!