Lecture 6. Fulton’s Trace Formula for Coherent Sheaf
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چکیده
A coherent F -module on X is a coherent sheafM on X, together with a Frobenius action onM, that is, a morphism of sheaves of OX-modules FM : M→ F∗(M). In other words, FM is a morphism of sheaves of Fq-vector spaces OX → OX such that FM(am) = aFM(m) for every a ∈ OX(U) and m ∈ M(U), where U is any open subset of X. As above, since FM is Fq-linear, it follows that it induces Fq-linear maps on cohomology that, abusing notation, we write FM : H (X,M)→ H (X,M). Despite the fact that FM is not
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