A note on the crystalline subrepresentation functor

丰塔内晶体函子的积分类似物

An integral analogue of Fontaine's crystalline functor

研究在完美域\(k\)上维特向量\(W\)上的光滑形式概型\(\mathfrak{X}\)，构造函子\(\mathbb{D}_{\mathrm{crys}}\)，证明其在特定条件下的性质及诱导范畴等价关系，还用它加强\(p -\)可除群的棱柱形迪厄多内理论研究。

A De Rham-Witt approach to crystalline rational homotopy theory

We construct the crystalline fundamental group of a semi-stable variety over a field of positive characteristic using the log De Rham-Witt complex and Navarro-Aznar's derived Thom-Whitney functor. This approach gives a relatively direct comparison theorem with the De Rham fundamental group in the liftable case. Also, we get a natural weight filtration which makes the coordinate ring of the crystalline fundamental group into a mixed isocrystal when the variety is defined over a finite field. Finally, the monodromy operator on the crystalline fundamental group is used to prove a crystalline anal…

Rank loci in representation spaces of quivers

Rank functors on a quiver $Q$ are certain additive functors from the category of representations of $Q$ to the category of finite-dimensional vector spaces. Composing with the dimension function on vector spaces gives a rank function on $Q$. These induce functions on $\rep(Q, α)$, the variety of representations of $Q$ of dimension vector $α$, and thus can be used to define "rank loci" in $\rep(Q, α)$ as collections of points satisfying finite lists of linear inequalities of rank functions. Although quiver rank functions are not generally semicontinuous like the rank of a linear map, we show he…

完备棱镜 $F$-晶体与晶体 $\u0000mathbf{Z}_p$-局部系统

Completed prismatic $F$-crystals and crystalline $\mathbf{Z}_p$-local systems

本文在光滑 $p$-进形式概形上引入完备棱镜 $F$-晶体，并证明其与晶体 étale $\mathbf{Z}_p$-局部系统范畴等价，推广了 Bhatt-Scholze 的结果。

de Rham 上同调函子的自同态

On endomorphisms of the de Rham cohomology functor

本文计算 de Rham 与晶体上同调函子的自同态模空间，并由此推导出 Drinfeld 对 Deligne--Illusie 分解的改进及进一步的函子性结论。

Smoothness of the truncated display functor

We show that to every p-divisible group over a p-adic ring one can associate a display by crystalline Dieudonne theory. For an appropriate notion of truncated displays, this induces a functor from truncated Barsotti-Tate groups to truncated displays, which is a smooth morphism of smooth algebraic stacks. As an application we obtain a new proof of the equivalence between infinitesimal p-divisible groups and nilpotent displays over p-adic rings, and a new proof of the equivalence due to Berthelot and Gabber between commutative finite flat group schemes of p-power order and Dieudonne modules over…