# Haoyang Guo

I am an L.E. Dickson instructor at the Univeristy of Chicago. Before that, I was a postdoc at the Max-Planck-Institut für Mathematik in Beethoven's hometown, Germany, from 2021 to 2023.

I am interested in algebraic geometry and number theory, especially p-adic geometry and p-adic Hodge theory.

I obtained my PhD in mathematics from the University of Michigan in the spring, 2021, where my advisor was Bhargav Bhatt. I got my bachelor degree from the University of Science & Technology of China in 2016.

Email: ghy "at" uchicago "dot" edu

Office: 332 Eckhart Hall.

Address: 5734 S. University Ave.,

Chicago, IL. 60637

## Papers/Preprints

Frobenius height of prismatic cohomology with coefficients, with Shizhang Li.

Preprint (2023), arXiv: 2309.06663 ,

Cohomological descent, de Rham comparison, and local acyclicity for some singular schemes, an appendix to

Rational p-adic Hodge theory for d-de Rham-proper stacks (by Dmitry Kubrak and Artem Prikhodko). Preprint (2022), arXiv: 2211.17227.

A prismatic approach to crystalline local systems, with Emanuel Reinecke.

Inventiones Mathematicae, Volume 236, pages 17–164, (2024), published version: link, arXiv: 2203.09490.

Prismatic cohomology of rigid analytic spaces over de Rham period's ring.

Preprint (2021), arXiv: 2112.14746.

Crystalline cohomology of rigid analytic spaces.

Preprint (2020), arXiv: 2112.14304.

Period sheaves via derived de Rham cohomology, with Shizhang Li.

Compositio Mathematica, Volume 157, Issue 11, November 2021, pp. 2377 - 2406, published version: link, arXiv: 2008.06143.

Hodge-Tate decomposition for non-smooth spaces.

J. Eur. Math. Soc. 25 (2023), no. 4, pp. 1553–1625, published version: link, arXiv: 1909.09917.

## Teachings

## @ University of Chicago:

Math 24200, Algebraic Number Theory (instructor): Spring 2024.

Math 15910, Introduction to Proofs in Analysis, two sections (instructor): Winter 2024.

Math 20310, Analysis in R^n I (instructor): Autumn 2023.

## @ University of Michigan:

Math 105 (instructor): Fall 2017, Winter 2018.

Math 115 (instructor): Fall 2018, Winter 2019, Fall 2020 (remote), Winter 2021 (remote).

Math 216 (lab instructor): Fall 2019; course instructor: Sofia Piltz.

Math 498, Representation theory (grader): Winter 2017; instructor: Jessica Fintzen.

Math 602, Functional analysis (grader): Fall 2016; instructor: Sijue Wu.

Math 676, Algebraic number theory (grader): Fall 2016; instructor: Kartik Prasanna.

## Expository Writings

Boundedness of semistable sheaves, with Sanal Shivaprasad, Dylan Spence, and Yueqiao Wu.

Stacks Project Expository Collection (London Mathematical Society Lecture Note Series), (2022), link, arXiv: 2112.03834.

On nearby cycle and perversity, an expository article on BBDG. Mar 2021. PDF.

HH, HKR; THH, and BMS 2, an expository article on (topological) Hochschild homology. May 2020. PDF.

Several approaches to Grothendieck duality. Jan 2020. PDF.

On the integral Hodge conjecture and integral Tate conjecture 3-folds, from a talk at Michigan. Dec 2019. PDF.

There is no abelian schemes over Z. Apr 2019. PDF.

Family of elliptic curves, and Serre-Tate theorem, from a talk at Michigan. Jun 2019. PDF.

Introduction to the de Jong's Alteration, from a talk at Michigan. Dec 2018. PDF.

Riemann-Zariski spaces and Nagata’s compactification, from a talk at Michigan. Oct 2018. PDF.

A note on de Jong’s conjecture, from a talk at Michigan. Jun 2018. PDF.

A mini-course on crystalline cohomology. Jun 2018. PDF.

F-finite modules, from a talk at Michigan. Mar 2018. PDF.

Note on finiteness properties of D-modules, from a talk at Michigan. Nov 2017. PDF.

"Spreading out” and its applications, from a talk at Michigan. Feb 2017. PDF.