发表机构
Işık University; İstanbul Technical University（伊什克大学; 伊斯坦布尔技术大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文受Igusa关系启发，为有界链复形上不交换微分的分级自同态构造泛商，迭代得极小滤过与平坦退化，使幂超迹由Lefschetz迹表示，给出对数行列式与zeta级数的同调表示。
AI 中文摘要
受Igusa关于相对循环同调与分级Cartan行列式对数之间关系的启发，我们分离了从对数行列式过渡到幂的迹背后的同调步骤。对于有界链复形$(C_*,d)$和次数为零的分级自同态$f$（不假定其与$d$交换），我们构造了使$f$成为链映射的泛商。该反射的核迭代产生典范函子性极小滤过，其Rees模给出向无曲率关联分级的平坦退化。对于有限维链群，$f$的所有幂超迹均由该关联分级上的Lefschetz迹表示，因此所得对数行列式和zeta级数具有典范同调表示。
英文摘要
Motivated by Igusa's relation between relative cyclic homology and the logarithm of the graded Cartan determinant, we isolate the homological step behind the passage from logarithmic determinants to traces of powers. For a bounded chain complex $(C_*,d)$ and a degree-zero graded endomorphism $f$, not assumed to commute with $d$, we construct the universal quotient on which $f$ becomes a chain map. The kernel of this reflection iterates to a canonical functorial minimal filtration, whose Rees module gives a flat degeneration to an uncurved associated graded. For finite-dimensional chain groups all power supertraces of $f$ are represented by Lefschetz traces on this associated graded, so the resulting logarithmic-determinant and zeta series admit a canonical homological representation.
Comments13 pages
