Singularities and vanishing cycles in number theory over function fields

与模曲线相关的Ceresa闭链和Gross--Kudla--Schoen闭链的非零性

Non-vanishing of Ceresa and Gross--Kudla--Schoen cycles associated to modular curves

本文研究模曲线对应的Ceresa闭链与Gross-Kudla-Schoen修正对角闭链的挠性问题，通过关联正交Shimura簇特殊闭链研究，推导特殊除子拉回公式，证明一大类模曲线的这两个闭链在对应Chow群中是非挠的。

On p-adic vanishing cycles of log smooth families

In this paper, we will show that the sheaf of p-adic vanishing cycles of a log smooth family over a DVR of mixed characteristic is generated by Milnor symboles. A key ingredient is a computation (due to K. Kato) on the graded quotients of a multi-indexed filtration on the sheaf concerned, which has been used in several papers of the first author.

Ceresa环的消失准则

Vanishing criteria for Ceresa cycles

本文研究了Ceresa环的消失准则，证明了在特定条件下，Ceresa环在Chow群中为 torsion，并探讨了Picard曲线的性质。

Filtration de monodromie et cycles evanescents formels

V.Berkovich, K.Fujiwara and R.Huber have proved independently by different methods that the fiber of the vanishing cycles at a point of the special fiber depends only on the formal completion at this point. We refine this result and prove the invariance under formal completion of the perverse monodromy filtration on the fiber of vanishing cycles. This result is used in an essential way by P.Boyer in his work on some "simple Shimura varieties".

分圆域中的奇消没圈

Odd vanishing cycles in cyclotomic fields

本文提出分圆域中Hecke群尖点的奇消没圈概念，刻画其轨道结构与对应单值群的性质，同时包含相关研究内容与综述内容。

The de Rham-Witt complex and p-adic vanishing cycles

We determine the structure modulo p of the de Rham-Witt complex of a smooth scheme X over a discrete valuation ring of mixed characteristic with log-poles along the special fiber Y and show that the sub-sheaf fixed by the Frobenius is isomorphic to the sheaf of p-adic vanishing cycles. We use this together with results of the second author and Madsen to evaluate the $K$-theory with finite coefficients of the quotient field K of the henselian local ring of X at a generic point of Y. The result affirms the Lichtenbaum-Quillen conjecture for the field K.

关于修正对角环与Ceresa环的Beauville分解

On Modified Diagonal Cycles and the Beauville Decomposition of the Ceresa Cycle

本文推广了Ceresa环的消失与对应Beauville分量、修正对角环消失的等价关系，建立逐次消失结果并应用于相关环的有理非平凡性，还给出整数层面的精细化结论。

Shimura 曲线的有限性性质与修正对角线环

Finiteness properties for Shimura curves and modified diagonal cycles

本文证明给定亏格界的 Shimura 曲线仅有有限多条，并猜想修正对角线环消失仅发生在有限多条曲线上，通过模形式数据与 Sage 计算给出分类结果和显式例子。

Arthur packets for $p$-adic groups by way of microlocal vanishing cycles of perverse sheaves, with examples

In this article we propose a geometric description of Arthur packets for $p$-adic groups using vanishing cycles of perverse sheaves. Our approach is inspired by the 1992 book by Adams, Barbasch and Vogan on the Langlands classification of admissible representations of real groups and follows the direction indicated by Vogan in his 1993 paper on the Langlands correspondence. Using vanishing cycles, we introduce and study a functor from the category of equivariant perverse sheaves on the moduli space of certain Langlands parameters to local systems on the regular part of the conormal bundle for …