مبرهنة توم-سباستياني

In complex analysis, a branch of mathematics, the Thom–Sebastiani Theorem states: given the germ ${\displaystyle{\displaystyle f:(\mathbb{C}^{n_{1}+n_{2}},0)\to(\mathbb{C},0)}}$ defined as ${\displaystyle{\displaystyle f(z_{1},z_{2})=f_{1}(z_{1})+f_{2}(z_{2})}}$ where ${\displaystyle{\displaystyle f_{i}}}$ are germs of holomorphic functions with isolated singularities, the vanishing cycle complex of ${\displaystyle{\displaystyle f}}$ is isomorphic to the tensor product of those of ${\displaystyle{\displaystyle f_{1},f_{2}}}$. Moreover, the isomorphism respects the monodromy operators in the sense: ${\displaystyle{\displaystyle T_{f_{1}}\otimes T_{f_{2}}=T_{f}}}$.

المبرهنة قدّمنها توم و سباستياني في 1971.

Observing that the analog fails in positive characteristic, Deligne suggested that, in positive characteristic, a tensor product should be replaced by a (certain) local convolution product.

 المراجع

• Illusie, Luc (24 April 2016). "Around the Thom-Sebastiani theorem". arXiv:1604.07004. {{cite journal}}: Cite journal requires |journal= (help)

قالب:Mathanalysis-stub