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- W2289667316 abstract "Let {V_l} be a strictly compatible rational system of Galois representations arising from geometry. Let V_l^ss be the semisimplification of V_l, V_l^ab the maximal abelian subrepresentation of V_l^ss, and G_l the algebraic monodromy group of V_l^ss. Conjecturally, the abelian part {V_l^ab} is again a strictly compatible rational system (Conj. Ab). This conjecture has meaningful consequences to arithmetic geometry, for example, the Tate conjecture is independent of l if Conj. Ab and the semisimplicity conjecture of Grothendieck hold. The main theme of this paper is to investigate Conj. Ab via l-independence of G_l. More precisely, we prove that Conj. Ab follows if (i) G_l is connected for all l, (ii) the tautological representation of the complex semisimple Lie group G_l^der(C) is independent of l, and (iii) the roots of G_l^der(C) meet a criterion (Thm. 1.3). These conditions are satisfied under some group theoretic assumptions of G_l (Thm. 1.5), for example, (ii) and (iii) hold if G_l^der(C) is connected and semisimple of type A_4+A_6+A_6 for some l; (iii) holds if G_l^der(C) is almost simple of type different form A_7,A_8,B_4,D_8." @default.
- W2289667316 created "2016-06-24" @default.
- W2289667316 creator A5071113396 @default.
- W2289667316 date "2016-03-03" @default.
- W2289667316 modified "2023-09-27" @default.
- W2289667316 title "Abelian part of compatible system and geometry of roots" @default.
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- W2289667316 hasPublicationYear "2016" @default.
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