By Kalantari I., Welch L.
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Extra resources for A blend of methods of recursion theory and topology: A П 0^1 tree of shadow points
3 we can diagonalize this matrix d over GLm (Op ∩ K Γ0 (p) ). But since G is irreducibel over GLm (Op ∩ K Γ0 (p) ) it follows, that d = ζσ Im , for a suitable root of unity ζσ . Now we have g σ = gζσ and at the same time g γ = gζγ for any γ ∈ Γ1 (p). Since Γ1 (p) k operates trivially on the p-th roots of unity ζ we obtain: g σ = g γ , for some integer k and therefore the two Galois automorphisms σ and γ k coincides on K Γ0 (p) (G1 ) since g is any generator of G1 . This gives the contradiction in the case, where g −1 g σ ∈ GLm (K Γ1 (p) ).
1) ι B• −−−−→ R ⊗O˜ A• commutes in D(S). We deﬁne a functor F : D(X) → T (X) setting F(C• ) = (π ∗ C• , S ⊗O C• , ι), where ι : R ⊗O C• is induced by the embedding S → R. Just as in S ⊗O C• → R ⊗O˜ (π ∗ C• ) Section 1 the following theorem holds (with almost the same proof, see ). 2. e. it is dense and conservative. Remark. We do not now whether it is full, though it seems to be true. 5. Configurations of type A and A˜ As it was shown in , even classiﬁcation of vector bundles is wild for almost all projective curves.
Note that a special word is never symmetric, a quasisymmetric word is always bispecial, and a bispecial word is always full. 6. We deﬁne a cycle as a word w such that r1 = rm−1 =∼ and xm − x1 . Such a cycle is called non-periodic if it cannot be presented in the form v − v − · · · − v for a shorter cycle v. For a cycle w we set rm = −, xqm+k = xk and rqm+k = rk for any q, k ∈ Z. 7. A (k-th) shift of a cycle w, where k is an even integer, is the cycle w[k] = xk+1 rk+1 xk+2 . . rk−1 xk . A cycle w is called symmetric if w[k] = w∗ for some k.
A blend of methods of recursion theory and topology: A П 0^1 tree of shadow points by Kalantari I., Welch L.