Classifying the Absolute Toral Rank Two Case by Helmut Strade

Author:Helmut Strade
Language: eng
Format: epub, pdf
Publisher: De Gruyter
Published: 2017-03-02T16:00:00+00:00

Pick u ∈ with Substituting u by u′ := u + λtα ∈ with a suitable λ ∈ F if necessary we get u′[p] = 0. But (ad u′)2(L(α)) ⊂ F tα, contradicting the rigidity of α. Thus = DH((1 + x1)x2). This means that α is improper (Theorem 11.2.5).

(3) Pick u1 ∈ with and observe that DH((1 + increases the x2-degree by p – 3. Argue as before to obtain 2(p − 3) – 1 ≤ p – 2, whence p = 5.

(4) Suppose H acts non-trigonalizably on L. Set Ω := {µ ∈ Γ(L, T) | µ(H(1)) ≠ 0}, which is non-empty by assumption. Proposition 1.3.6 (with Γ0 := Γ(L, T) \ Ω) shows that Ω contains a root κ independent of α. Since every irreducible H-module has p-power dimension and (iκ)(H(1)) ≠ 0 for all dim Liκ ≥ p = 5. Next observe that

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