Most of the papers below have some connection to Witt vectors, but as of March 2022, I am making a concerted effort to branch out!

Here is a link to my papers on arXiv.

## Publications

On the de Rham-Witt complex over perfectoid rings, with Irakli Patchkoria. To appear in International Mathematics Research Notices. Version of March 21, 2021.

On the p-typical de Rham-Witt complex over W(k). Alg. Number Th. 13 (2019) 1597-1631. Version of April 21, 2019.

Explicit points on y^2 + xy + (t^d)y = x^3 and related character sums, with Tommy Occhipinti. J. Number Theory. 168 (2016), 13-38. Version of 9/26/2014.

Newton slopes for Artin-Schreier-Witt towers, with Daqing Wan and Liang Xiao. Math. Ann. 364 (2016), no. 3-4, 1451-1468. Version of 10/20/2013.

A characterization of strictly APF extensions, with Bryden Cais and Jonathan Lubin. J. Théor. Nombres Bordeaux. 28 (2016), no. 2, 417-430. Version of 2/20/2014.

Almost purity and overconvergent Witt vectors, with Kiran Kedlaya. J. Algebra. 422 (2015), 373-412. Version of 8/16/2014.

Canonical Cohen rings for norm fields, with Bryden Cais. Int. Math. Res. Not. 2015 (2015), 5473-5517. Version of 12/30/2013.

Integral structure on Monsky-Washnitzer cohomology and the overconvergent de Rham-Witt complex, with David Zureick-Brown. Math. Res. Lett. 21 (2014), no. 2, 281-288. Version of 5/1/2013.

Which finite simple groups are unit groups?, with Tommy Occhipinti. J. Pure Appl. Algebra 218 (2014), no. 4, 743-744. Version of 8/6/2013.

Which alternating and symmetric groups are unit groups?, with Tommy Occhipinti. J. Algebra Appl. 13 (2014), 12 pp. Version of 7/16/2013.

L-functions of p-adic characters, with Daqing Wan. Nagoya Math. J. 213 (2014), 77-104. Version of 3/30/2013.

On the Witt vector Frobenius, with Kiran Kedlaya. Proc. Amer. Math. Soc. 142 (2014), 2211-2226. Version of 10/1/2012.

Overconvergent Witt vectors, with Andreas Langer and Thomas Zink. J. Reine Angew. Math. 668 (2012), 1-34.

Overconvergent de Rham-Witt cohomology, with Andreas Langer and Thomas Zink. Ann. Scient. Éc. Norm. Sup. (4) 44 (2011), no. 2, 197-262. The overconvergent de Rham-Witt complex, Ph.D. Thesis, MIT. Advised by Kiran Kedlaya. 2009. You can see it here by clicking on the “Preview, non-printable” link. However, note that the results of the first four sections are improved and expanded in my joint papers with Andreas Langer and Thomas Zink, and the results of the last two sections are improved and expanded in my joint papers with Kiran Kedlaya.

Totally geodesic Seifert surfaces in hyperbolic knot and link complements II (access by subscription), with Colin Adams, Hanna Bennett, Michael Jennings, Jennifer Novak, Nicholas Perry, and Eric Schoenfeld. J. Differ. Geom. 79 (2008), no. 1, 1-23.

## Preprints

Witt vectors with p-adic coefficients and Fontaine’s rings, with Kiran Kedlaya. Version of 2/21/11. Much of this material has been moved into our papers *On the Witt vector Frobenius* and *Almost purity for overconvergent Witt vectors*.