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Some remarks on the smash-nilpotence conjecture 关于粉碎零势猜想的一些评论
Pub Date : 2024-06-01 DOI: 10.1016/j.indag.2024.05.009
Bruno Kahn
We discuss cases where Voevodsky’s smash nilpotence conjecture is known, and give a few new ones. In particular we explain a theorem of the cube for 1-cycles, which is due to Oussama Ouriachi.
我们讨论了 Voevodsky 的粉碎零势猜想已知的情况,并给出了一些新情况。特别是,我们解释了欧萨马-乌里亚奇(Oussama Ouriachi)提出的关于 1 循环的立方体定理。
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引用次数: 0
Chow–Lefschetz motives 周-莱夫谢茨动机
Pub Date : 2024-05-03 DOI: 10.1016/j.indag.2024.04.007
Bruno Kahn
We develop Milne’s theory of Lefschetz motives for general adequate equivalence relations and over a not necessarily algebraically closed base field. The corresponding categories turn out to enjoy all properties predicted by standard and less standard conjectures, in a stronger way: algebraic and numerical equivalences agree in this context. We also compute the Tannakian group associated to a Weil cohomology in a different and more conceptual way than Milne’s case-by-case approach.
我们发展了米尔恩关于一般充分等价关系和不一定代数闭合基域的列夫谢茨动机理论。结果证明,相应的范畴享有标准猜想和非标准猜想所预言的所有性质,而且以更强的方式:代数等价和数字等价在这种情况下是一致的。我们还以一种不同于米尔恩的逐个方法、更概念化的方式计算了与魏尔同调相关的坦纳基群。
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引用次数: 0
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Indagationes Mathematicae
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