An Overview of the Decomposition Theorem
نویسنده
چکیده
Here we briefly sketch the original proof of [BBD]. The main reference of this talk would be [dCM1], the expository article for this subject written by de Cataldo and Migliorini. The main idea of [BBD] is that first we prove this theorem over a finite field and use ”spread out” principle. One of the important property of this method is that we have an action of the Galois group which acts on varieties and sheaves, which is topologically generated by the Frobenius morphism. Here we introduce the notion of weights ; it is basically the absolute value of its eigenvalues. If the weights of some complex is in sufficiently good shape, we call it mixed/pure, and we will see that it indeed gives a rigid structure on such complexes and morphisms between them.
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