具有有限系数的混合Artin-Tate motive
K理论与同调
2014-04-28 v6 代数几何
范畴论
摘要
本文的目标是给出具有有限系数Z/m的Tate和Artin-Tate motive的三角范畴的显式描述，这些motive定义在包含本原m次单位根的域K上，作为K的绝对伽罗瓦群上具有对逐次商特定限制的滤过模的精确范畴的导出范畴。该描述是有条件的（其有效性等价于）关于K的米尔诺K-理论/伽罗瓦上同调的某些Koszul性假设。本文还旨在解释任意非负分次环为Koszul的含义。附录中讨论了精确范畴、愚蠢滤过和K(π,1)猜想。在“结论”部分考虑了具有整系数的Tate motive。
引用
@article{arxiv.1006.4343,
title = {Mixed Artin-Tate motives with finite coefficients},
author = {Leonid Positselski},
journal= {arXiv preprint arXiv:1006.4343},
year = {2014}
}
备注
LaTeX 2e with pb-diagram.sty, 88 pages, 6+1 commutative diagrams; v.3: additions in the "conclusions" section, other small improvements; v.4: subsection 0.14 inserted in the Introduction, corollary added in subsection 7.3, section 9 expanded; v.5: two references added, several misprints corrected -- this is intended as the final version; v.6: several misprints corrected in section 4