A study of arithmetic varieties

主要研究者在管状邻域和上同调下降的关键词下研究了各种正特征的上同调理论。主要内容如下：（1）单纯簇管状邻域的构造;（2）刚性上同调的上同调下降（部分与Chiarellotto合作），（3）正常态射和光滑态射的相对刚性上同调的通有有限性，（4）de Rham上同调和Hodge滤的上同调下降（与Chiarellotto合作），（5）单纯族的刚性和de Rham上同调之间的比较图，Kato研究了（1）Mumford曲线和覆盖为Mumford曲线的p-adic orbifold（与Cornelissen合作），（2）刚性解析空间的基础（与藤原合作）。木村研究了动机的有限维度。伊藤工作的算法计算数量合理点的品种在有限领域的首席调查员。杉山研究（1）BSD型问题的Selberg Zeta函数的三维流形和（2）几何模拟的朗兰兹对应。Shiho发展了（1）晶体基本群理论和（2）使用对数晶体上同调的权重理论。Sumida研究了数域的几个Iwasawa不变量。田口的结果有限的伽罗瓦表示与某些条件（与月亮），。他还致力于快速算法计算数量的合理点的椭圆曲线在有限领域（与佐藤），。

The head investigator studied the cohomology theories for varieties of positive characteristic under the key words : tubular neighborhoods and cohomological descent. The contents are as follow ; (1)Construction of tubular neighborhoods of simplicial varieties, (2)Cohomological descent in rigid cohomology (partially collaborated with Chiarellotto), (3)Generic finiteness of relative rigid cohomology for proper and smooth morphisms, (4)Cohomological descent in de Rham cohomology and Hodge filtrations (collaborated with Chiarellotto), (5)Comparison map between rigid and de Rham cohomologies for simplicial families, and (6)Purity theorem for overconvergent isocrystals.Kato studied (1)Mumford curves and p-adic orbifolds with a covering which are Mumford curves (collaborated with Cornelissen), and (2)the foundations of rigid analytic spaces (collaborated with Fujiwara). Kimura studied the finite dimensionality of motives. Ito worked on algorithms of computing numbers of rational points of varieties over finite fields with the head investigator. Sugiyama studied (1)the BSD type problem in the Selberg Zeta functions for 3-dimentional manifolds and (2)a geometric analogue of Langlands correspondence. Shiho developed (1)the theory of crystalline fundamental group and (2)the theory of weights using logarithmic crystalline cohomology. Sumida studied several Iwasawa invariants for number fields. Taguchi had results on the finiteness of Galois representations with certain conditions (collaborated with Moon),. He also worked on the fast algorithm for computing numbers of rational points of elliptic curves over finite fields (collaborated with Sato),.