AI 中文总结
本文研究t-平精细对数概形，确定其深度由对数分层决定，建立其对数余切复形理论并给出t-平性的同调判据，丰富了对数几何的相关基础理论。
AI 中文摘要
我们建立了t-平精细对数概形的一些基本性质，即其基础概形在合适意义下相对于其对数结构是平的精细对数概形。值得注意的是，我们证明了t-平fs对数概形的深度可由其对数分层直接确定。我们还证明了t-平精细对数概形存在良好的对数余切复形理论，并利用该对数余切复形给出了t-平性的同调判据。
英文摘要
We establish some basic properties of t-flat fine log schemes, i.e., fine log schemes whose underlying schemes are flat over their log structure (in a suitable sense). Notably, we show that the depth of a t-flat fs log scheme is simply determined by its logarithmic stratification. We also show that there is a good theory of log cotangent complexes for t-flat fine log schemes, and use the log cotangent complex to give a homological criterion for t-flatness.
Comments30 pages, comments welcome
