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It is a theorem of Deligne that this is essentialy the only possible formula if you ask for the determinant functor to satisfy some natural properties (mainly det has to be compatible with exact sequences). See these Slides by Fernando Muro for example.

It is a theorem of Deligne that this is essentialy the only possible formula if you ask for the determinant functor to satisfy some natural properties (mainly det has to be compatible with exact sequences). See these slides by Fernando Muro for example.

It is a theorem of Deligne that this is essentialy the only possible formula if you ask for the determinant functor to satisfy some natural properties (mainly det has to be compatible with exact sequences). See these Slides by Fernando Muro for example.

It is a theorem of Deligne that this is essentialy the only possible formula if you ask for the determinant functor to satisfy some natural properties (mainly det has to be compatible with exact sequences). See these Slides by Fernando Muro for example.

It is a theorem of Deligne that this is essentialy the only possible formula if you ask for the determinant functor to satisfy some natural properties (mainly det has to be compatible with exact sequences). See theses Slides for example.

It is a theorem of Deligne that this is essentialy the only possible formula if you ask for the determinant functor to satisfy some natural properties (mainly det has to be compatible with exact sequences). See these Slides by Fernando Muro for example.