Birational smooth minimal models have equal Hodge numbers in all dimensions

曲面的torsion birational motives与unramified cohomology

Torsion birational motives of surfaces and unramified cohomology

该研究探讨了曲面的torsion birational motives与unramified cohomology的关系，并扩展了Kahn的结果，同时给出了违反积分Hodge猜想的例子。

Period Spaces for Hodge Structures in Equal Characteristic

We develop the analog in equal positive characteristic of Fontaine's theory for crystalline Galois representations of a p-adic field. In particular we describe the analog of Fontaine's functor which assigns to a crystalline Galois representation an isocrystal with a Hodge filtration. In equal characteristic the role of isocrystals and Hodge filtrations is played by z-isocrystals and Hodge-Pink structures. The latter were invented by Pink. Our first main result in this article is the analog of the Colmez-Fontaine Theorem that "weakly admissible implies admissible". Next we construct period spac…

Structures de Hodge-Pink pour les $φ/\mathfrak S$-modules de Breuil et Kisin

In this article, we apply the methods of our work on Fontaine's theory in equal characteristics to the $φ/\mathfrak S$-modules of Breuil and Kisin. Thanks to a previous article of Kisin, this yields a new and rather elementary proof of the theorem "weakly admissible implies admissible" of Colmez-Fontaine.

Topological Hochschild homology and integral $p$-adic Hodge theory

In mixed characteristic and in equal characteristic $p$ we define a filtration on topological Hochschild homology and its variants. This filtration is an analogue of the filtration of algebraic $K$-theory by motivic cohomology. Its graded pieces are related in mixed characteristic to the complex $AΩ$ constructed in our previous work, and in equal characteristic $p$ to crystalline cohomology. Our construction of the filtration on $\mathrm{THH}$ is via flat descent to semiperfectoid rings. As one application, we refine the construction of the $AΩ$-complex by giving a cohomological construction o…