The Stacks project

1.2 Attribution

The scope of this work is such that it is a daunting task to attribute correctly and succinctly all of those mathematicians whose work has led to the development of the theory we try to explain here. We hope eventually to generate enough community interest to find contributors willing to write sections with historical remarks for each and every chapter.

Those who contributed to this work are listed on the title page of the book version of this work and online. Here we would like to name a selection of major contributions:

1. Jarod Alper contributed a chapter discussing the literature on algebraic stacks, see Guide to Literature, Section 112.1.

2. Bhargav Bhatt wrote the initial version of a chapter on étale morphisms of schemes, see Étale Morphisms, Section 41.1.

3. Bhargav Bhatt wrote the initial version of More on Algebra, Section 15.89.

4. Kiran Kedlaya contributed the initial writeup of Descent, Section 35.4.

5. The initial versions of

   1. Algebra, Section 10.28,

   2. Injectives, Section 19.2, and

   3. the chapter on fields, see Fields, Section 9.1.

   are from The CRing Project, courtesy of Akhil Mathew et al.

6. Alex Perry wrote the material on projective modules, Mittag-Leffler modules, including the proof of Algebra, Theorem 10.95.6.

7. Alex Perry wrote the chapter on deformation theory a la Schlessinger and Rim, see Formal Deformation Theory, Section 90.1.

8. Thibaut Pugin, Zachary Maddock and Min Lee took notes for a course which formed the basis for a chapter on étale cohomology and a chapter on the trace formula. See Étale Cohomology, Section 59.1 and The Trace Formula, Section 64.1.

9. David Rydh has contributed many helpful comments, pointed out several mistakes, helped out in an essential way with the material on residual gerbes, and was the originator for the material in More on Groupoids in Spaces, Sections 79.12 and 79.15.

10. Burt Totaro contributed Examples, Sections 110.64, 110.65, and Properties of Stacks, Section 100.12.

11. The chapter on pro-étale cohomology, see Pro-étale Cohomology, Section 61.1, is taken from a paper by Bhargav Bhatt and Peter Scholze.

12. Bhargav Bhatt contributed Examples, Sections 110.71 and 110.75.

13. Ofer Gabber found mistakes, contributed corrections and he contributed Varieties, Lemma 33.7.17, Formal Spaces, Lemma 87.14.7, the material in More on Groupoids, Section 40.15, the main result of Properties of Spaces, Section 66.17, and the proof of More on Flatness, Proposition 38.25.13.

14. János Kollár contributed Algebra, Lemma 10.119.2 and Local Cohomology, Proposition 51.8.7.

15. Kiran Kedlaya wrote the initial version of More on Algebra, Section 15.90.

16. Matthew Emerton, Toby Gee, and Brandon Levin contributed some results on thickenings, in particular More on Morphisms of Stacks, Lemmas 106.3.7, 106.3.8, and 106.3.9.

17. Lena Min Ji wrote the initial version of More on Algebra, Section 15.125.

18. Matthew Emerton and Toby Gee wrote the initial versions of Geometry of Stacks, Sections 107.3 and 107.5.