Tamely ramified torsors and parabolic bundles

An embedding problem for finite local torsors over twisted curves

“…Biswas–Borne showed that finite flat torsors which are representable by a k ‐scheme over root stacks give candidates of tamely ramified torsors (cf. [7, §3.3]; see also Theorem 4.15(1)). Hence, Question 1.6 has the following interpretation, but the author is not sure if these are equivalent to each other (cf.…”

“…Note that if Question 1.6 has an affirmative answer, then so does Question 1.7 (cf. [7, §3.3]; see also Theorem 4.15(1)). Toward the strong analogue, we shall study an embedding problem over the root stacks and conclude that Question 1.7 has an affirmative answer at least in the solvable case.…”

“…In [7], Biswas–Borne introduced the notion of tamely ramified G ‐torsors for an arbitrary finite group scheme G as a generalization of tamely ramified Galois covers in the usual sense (cf. Definition 4.14).…”

“…For an affine group scheme G over a field k , we denote by the derived subgroup of G (cf. [40, §10.1], [7, Definition A.1]). Then it turns out that the quotient is abelian and the natural surjection is universal among morphisms into abelian k ‐group schemes (cf.…”

“…Then it turns out that the quotient is abelian and the natural surjection is universal among morphisms into abelian k ‐group schemes (cf. [7, Appendix §A.1]). In particular, G is abelian if and only if .…”