## Download Anonymous File Sharing and Darknet - How to Be a Ghost in by Lance Henderson PDF

By Lance Henderson

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C) For ∆j = (π ∗ Dj )red we have r ∗ π D= j=1 N · αj · ∆j . gcd(N, αj ) d) If Y is irreducible then the components of ∆j have over Dj the ramiﬁcation index N ej = . gcd(N, αj ) Proof: For a) we can consider the open set Spec B ⊂ X − Dred . Hence Spec B[t]/tN −u is in Y dense and open. Y is reducible if and only if tN − u is reducible in B[t], which is equivalent to the existence of some u ∈ B with µ u=u . 13) part a) and b). For c) and d) we may assume that D = α1 · D1 and, splitting the covering in 28 H.

4,d). Hence we ﬁnd a divisor C > 0 and µ > 0 with Lµ (−C) ample. 1) H b (X, L−1 ⊗ (L−N ·ν−µ (ν·D + C))η ) = 0 for b < n and for η suﬃciently large. 13) this condition is compatible with blowing ups. Hence we may assume D + C to be a normal crossing divisor and, choosing ν large enough, we may again assume that the multiplicities of D = ν·D + C are smaller than N = N ·ν + µ. Replacing D and N by some high multiple we can assume in addition that LN (−D ) is generated by global section and that H b (X, L−N −1 (D )) = 0 for b < n.

Proof (see [22]): The sheaves Ra g∗ V are analytically constructible sheaves ([61]) and their support Sa = Supp(Ra g∗ V ) must be a Stein space, hence H b (W, Ra g∗ V ) = 0 for b > dim Sa . However, the general ﬁbre of g |g−1 (Sa ) must have a dimension larger than or equal to a2 . Hence 2 · (dim g −1 (Sa ) − dim Sa ) ≥ a and H b (W, Ra g∗ V ) = 0 for a + b > n + r(g) ≥ 2 · dim g −1 (Sa ) − dim Sa ≥ a + dim Sa . 13). ✷ 42 H. Esnault, E. 14. Remark. 6) one has cd(X, D) = dim U − 1, whereas r(g) = dim U − 2.