Papers

In the interest of keeping things consistent, it is best to download arxived copies if you are interested in the free public versions of the following papers. However, please note that arxiv files and the final published versions may not be identical. (At the very least, changes made to page proofs will not be reflected in these versions of the files.) A couple of files are not on the arxiv and may be directly linked at a later date. "In preparation" means that a rough draft is not yet complete and may not be for some time. "Coming soon" means that a draft will be complete within a month (or maybe not). "Preprint (being revised)" means that there is a complete document which is being debugged. "Preprint" means that the document is (at the moment) complete and has at least limited circulation; most of these will be on the arxiv. The strict meanings of these words are really just fantasies. (I don’t think I follow these rules anymore.)

1. Moduli of twisted sheaves and generalized Azumaya algebras, Oberwolfach Reports, Vol. 1, Issue 3 (2004)

2. Groupoids and quotients in algebraic geometry, Snowbird lectures in algebraic geometry, Contemp. Math. 388 (2005), 119–136

3. (with Charles Cadman, Izzet Coskun, Kelly Jabbusch, Michael Joyce, Sándor Kovács, Fumitoshi Sato, Matt Szczesny, and Jing Zhang) A first glimpse at the minimal model program, Snowbird lectures in algebraic geometry, Contemp. Math. 388 (2005), 17–42

4. Moduli of complexes on a proper morphism, J. Algebraic Geom. 15 (2006), 175–206

5. Remarks on the stack of coherent algebras, Internat. Math. Res. Notices, vol. 2006, Article ID 75273.

6. Moduli of twisted sheaves, Duke Math. J., Volume 138, Number 1 (2007), 23–118.

7. Twisted sheaves and the period-index problem, Compos. Math., Vol. 144 Part 1 (2008) 1–31

8. Openness of tilted hearts, appendix to Bridgeland-Stable Moduli Spaces for K-Trivial Surfaces, by D. Arcara and A. Bertram

9. (with Sándor Kovács) Boundedness of families of canonical ly polarized manifolds: A higher dimensional analogue of Shafarevich’s conjecture, submitted

10. Period and index in the Brauer group of an arithmetic surface, with an appendix by Daniel Krashen, submitted

11. (with Martin Olsson) Generators and relations for the ´etale fundamental group, submitted

12. (with Daniel Krashen) Brauer index reduction via stable sheaves, with an appendix by Bhargav Bhatt, Int Math Res Notices (2008) Vol. 2008, article ID rnn010

13. (with Brian Osserman) Functorial reconstruction theorems for stacks, preprint

14. Arithmetic aspects of moduli spaces of vector bundles, in preparation

15. Compactified moduli of projective bundles, submitted

16. Moduli of twisted orbifold sheaves, preprint

17. (with Brian Conrad, A. J. de Jong, and Martin Olsson) Absolute Noetherian approximation and Nagata compactification for algebraic spaces, in preparation


Books

1. (with Brian Conrad) Galois representations arising from p-divisible groups, book in preparation

2. (with A. J. de Jong, Roya Beheshti, Alexandru Ghitza, and Damiano Testa) Elliptic Surfaces and Azumaya Algebras, book in preparation

3. (with Martin Olsson, Brian Osserman, and Ravi Vakil) Deformation theory in algebraic geometry, book in preparation