Poincare series and miraculous duality

The Auslander-Reiten quiver of a Poincare duality space

In a previous paper, math.AT/0304079, Auslander-Reiten triangles and quivers were introduced into algebraic topology. This paper shows that over a Poincare duality space, each component of the Auslander-Reiten quiver is isomorphic to ZA_{\infty}.

模 $p$ 皮卡定理对于 $p$-adic 周期域

Mod $p$ Poincaré duality for $p$-adic period domains

本文提出了一类满足模 $p$ 皮卡定理的 $p$-adic 周期域，恢复了几乎良好概形的皮卡定理并推广了德林费尔德对称空间的上同调计算。

Calabi-Yau categories and Poincare duality spaces

The singular cochain complex of a topological space is a classical object. It is a Differential Graded algebra which has been studied intensively with a range of methods, not least within rational homotopy theory. More recently, the tools of Auslander-Reiten theory have also been applied to the singular cochain complex. One of the highlights is that by these methods, each Poincare duality space gives rise to a Calabi-Yau category. This paper is a review of the theory.