Syntomic complexes and $p$-adic étale Tate twists

正特征下合成上同调的局部塔特对偶

Local Tate duality for syntomic cohomology in positive characteristic

本文针对特征p>0的局部域k，证明带系数且基于Dodd的F-规范理论的合成上同调满足局部塔特对偶，还得到其整数环上合成上同调的拉格朗日性质，p>2时可导出相关经典对偶与正交性结果。

Syntomic cohomology and Beilinson's Tate conjecture for $K_2$

In this paper, we study an analogue of the Tate conjecture for $K_2$ of U, the complement of split multiplicative fibers in an elliptic surface. A main result is to give an upper bound of the rank of the Galois fixed part of the etale cohomology $H^2(\bar{U},Q_p(2))$. As an application, we give an elliptic K3 surface $X$ over a p-adic field for which the torsion part of the Chow group $CH_0(X)$ of 0-cycles is finite. This would be the first example of a surface $X$ over a p-adic field whose geometric genus is non-zero and for which the torsion part of $CH_0(X)$ is finite.

Syntomic cohomology and $p$-adic motivic cohomology

We prove a mixed characteristic analog of the Beilinson-Lichtenbaum Conjecture for p-adic motivic cohomology. It gives a description, in the stable range, of p-adic motivic cohomology (defined using algebraic cycles) in terms of differential forms. This generalizes a result of Geisser from small Tate twists to all twists and uses as a critical new ingredient the comparison theorem between syntomic complexes and p-adic nearby cycles proved recently in Colmez-Niziol.

$p$-adic étale Tate 扭转的 Gersten 猜想与 $p$-adic 循环类映射

The Gersten conjecture for $p$-adic étale Tate twists and the $p$-adic cycle class map

本文证明了混合特征光滑概形上 $p$-adic étale Tate 扭转的 Gersten 猜想，并推广了循环类映射至任意有限剩余域。

完美$F$-规范与有限平坦群概形

Perfect $F$-gauges and finite flat group schemes

该研究建立了$p$-进基上有限局部$p^n$-挠交换群概形与特定完美$F$-规范中模的范畴等价，推导了相对fppf上同调可表性等推论，还给出通用分类准则以复现及拓展相关分类结果。

$p$-adic Periods 和 Selmer 方案图像

$p$-adic Periods and Selmer Scheme Images

本文旨在为扩展Chabauty-Kim方法到更一般的超曲线上奠定基础，通过定义更一般的$p$-adic周期映射和非交换Chabauty框架，连接$p$-adic迭代积分与Goncharov的动机迭代积分理论。