Coming soon!
My Master thesis. It surveys the result of Bhatt-Scholze on the equivalence between the category of derived Laurent prismatic F-crystals over a quasisyntomic p-adic formal scheme and that of derived proétale local systems (i.e. lisse complexes of proétale sheaves) over its rigid generic fiber.
Affine Representability in Unstable Motivic Homotopy Theory (in Chinese, available upon request), with slides
My Bachelor thesis. It surveys the result of Asok-Hoyois-Wendt which says although the moduli stack of vector bundles is not A1-invariant, it behaves as if it is (A1-invariant and) represented by the infinite Grassmannian in the unstable motivic homotopy category when tested against affine schemes.
Notes and slides for a talk at UCSD arXiv seminar in Winter 2024. It explains a result of Bachmann which says the p-localization of the stable motivic category of every char p scheme is tensored over the derived category of abelian groups.
Notes for a talk at UCSD arXiv seminar in Fall 2023. A not-so-brief summary for the series of works of Ben Moshe, Carmeli, Schlank and Yanovski on the telescope ambidexterity, semiadditive height and semiadditive algebraic K-theory, with an emphasis on their relation to the redshift phenomena for chromatically localized algebraic K-theory.
Notes and slides for a talk at UCSD topology seminar in Fall 2022. It explains the categorical foundations and computational examples for naive equivariant spectra and Bredon cohomology, together with an application to the proof of Smith theorem (the fixed point of a p group action on a mod p cohomology sphere is either empty or another mod p cohomology sphere).
Notes for a talk at Orsay in Spring 2022. It explains how to prove flat descent of the quasicoherent derived category via Mathew's theory of descendability (plus Scholze's observation on the ω1 accessibility of faithfully flat ring maps).