I am an associate professor in the Department of Mathematics at Yale. My research is in algebraic geometry and its relations to number theory and homological algebra. I received my PhD from Harvard in 2022.
e-mail: alexander.petrov.57 at gmail dot com
My CV.
Yale Algebraic and Arithmetic Geometry Seminar, Mondays 4:30-6pm in KT 801
Papers and preprints
-
(with Bogdan Zavyalov) Formality for rigid-analytic spaces satisfying the weight-monodromy conjecture,
pdf,
arXiv:2607.14517.
-
Decomposition of de Rham complex for quasi-F-split varieties,
pdf,
arXiv:2502.13356.
-
(with Alexei Skorobogatov) On spectral sequences for semiabelian varieties over non-closed fields,
pdf,
arXiv:2411.15353.
-
appendix to 'Boundedness of the p-primary torsion of the Brauer group of products of varieties' by Alexei Skorobogatov,
pdf,
arXiv:2404.19150.
-
Non-decomposability of the de Rham complex and non-semisimplicity of the Sen operator, to appear in Annals of Mathematics,
pdf,
arXiv:2302.11389.
-
Universality of the Galois action on the fundamental group of 𝐏1\{0,1,∞}, to appear in JEMS,
pdf,
arXiv:2109.09301.
-
appendix to 'Hodge numbers are not derived invariants in positive characteristic' by Nicolas Addington and Daniel Bragg,
Mathematische Annalen,
arXiv:2106.09949,
journal.
-
Geometrically irreducible p-adic local systems are de Rham up to a twist,
Duke Math. J.,
pdf,
arXiv:2012.13372,
journal.
-
Rigid-analytic varieties with projective reduction violating Hodge symmetry,
Compositio Mathematica,
pdf,
arXiv:2005.02226,
journal.
-
(with Vadim Vologodsky) On the periodic topological cyclic homology of DG categories in characteristic p,
pdf,
arXiv:1912.03246.
-
(with Dmitry Vaintrob and Vadim Vologodsky) The Gauss-Manin connection on the periodic cyclic homology, Selecta Mathematica,
pdf,
arxiv:1711.02802,
journal.
Other writing
-
Notes on de Rham cohomology and D-modules in mixed characteristic, course 18.708, February 2026 pdf
-
Arithmetic local systems and p-adic Hodge theory, survey for the proceeding of the 2025 SRI Algebraic Geometry
Bootcamp,
pdf of the first version.
-
Notes on non-abelian Hodge theory in positive characteristic, after A. Ogus, V. Vologodsky, for 'Complex and p-Adic Simpson Correspondence'
workshop at Brin Center, November 2025,
pdf.
-
(report on joint work with Lue Pan) Characteristic classes of étale local systems, Oberwolfach Report for 'Anabelian Geometry and Representations of Fundamental Groups' workshop, October 2024,
pdf,
volume.