论文标题
相同的代数空间和分析空间相同特征零的相对最小模型程序
The relative minimal model program for excellent algebraic spaces and analytic spaces in equal characteristic zero
论文作者
论文摘要
我们建立了相对最小模型程序，并通过缩放为准的代数空间的投射形态，以承认双重化合物，准级别的正式方案，正式的正式方案，复杂的分析空间的半脱种植，刚性分析空间，刚性分析空间，Berkovich空间，berkovich空间以及弱点的范围均等范围均等范围，均等范围。为此，我们证明了使用Cascini andLazić的策略以及Kawamata-Viehweg的概括将定理的定理与第二作者最近建立的方案设置有关。为了统一证明这些结果，我们证明了Gaga定理的二元性和双重化合物，以减少代数情况。此外，我们应用我们的方法来建立相对最小的模型程序，并以尺寸为dimensions $ \ le 3 $在正面和混合特征中缩放上述形式的空间，并表明一个人可以在每个步骤中运行相对最小的模型程序，并在不缩小基础的情况下使用缩放复杂的分析空间。
We establish the relative minimal model program with scaling for projective morphisms of quasi-excellent algebraic spaces admitting dualizing complexes, quasi-excellent formal schemes admitting dualizing complexes, semianalytic germs of complex analytic spaces, rigid analytic spaces, Berkovich spaces, and adic spaces locally of weakly finite type over a field, all in equal characteristic zero. To do so, we prove finite generation of relative adjoint rings associated to projective morphisms of such spaces using the strategy of Cascini and Lazić and the generalization of the Kawamata-Viehweg vanishing theorem to the scheme setting recently established by the second author. To prove these results uniformly, we prove GAGA theorems for Grothendieck duality and dualizing complexes to reduce to the algebraic case. In addition, we apply our methods to establish the relative minimal model program with scaling for spaces of the form above in dimensions $\le 3$ in positive and mixed characteristic, and to show that one can run the relative minimal model program with scaling for complex analytic spaces without shrinking the base at each step.
