Monodromy Group for a Strongly Semistable Principal Bundle over a Curve, Ii
نویسندگان
چکیده
Let X be a geometrically irreducible smooth projective curve defined over a field k. Assume that X has a k–rational point; fix a k–rational point x ∈ X . From these data we construct an affine group scheme GX defined over the field k as well as a principal GX–bundle EGX over the curve X . The group scheme GX is given by a Q–graded neutral Tannakian category built out of all strongly semistable vector bundles over X . The principal bundle EGX is tautological. Let G be a linear algebraic group, defined over k, that does not admit any nontrivial character which is trivial on the connected component, containing the identity element, of the reduced center of G. Let EG be a strongly semistable principal G–bundle over X . We associate to EG a group scheme M defined over k, which we call the monodromy group scheme of EG, and a principal M–bundle EM over X , which we call the monodromy bundle of EG. The group scheme M is canonically a quotient of GX , and EM is the extension of structure group of EGX . The group scheme M is also canonically embedded in the fiber Ad(EG)x over x of the adjoint bundle.
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