71 citations · 87 across the 9 of their papers we have counts for
10 papers
Parabolic opers and differential operators
Indranil Biswas, Niels Borne, Sorin Dumitrescu +2
Parabolic SL(r,C)-opers were defined and investigated in [BDP] in the set-up of vector bundles on curves with a parabolic structure over a divisor. Here we introduce and study holo…
Parabolic connections and stack of roots
Niels Borne, Amine Laaroussi
Given a scheme over a field endowed with a strict normal crossings divisor, we define strongly parabolic connections, consistently with the current terminology for Higgs bundles. W…
Tamely ramified torsors and parabolic bundles
Indranil Biswas, Niels Borne
Given a variety , and a normal crossings divisor , we relate, in the case of abelian monodromy, the following two: 1. existence of a -torsor with prescribed ramif…
Fundamental gerbes
Niels Borne, Angelo Vistoli
For a class of affine algebraic groups over a field, we define the notions of -fundamental gerbe of a fibered category, generalizing what we had done in ar…
The Nori fundamental gerbe of tame stacks
Indranil Biswas, Niels Borne
Given an algebraic stack, we compare its Nori fundamental group with that of its coarse moduli space. We also study conditions under which the stack can be uniformized by an algebr…
Lifting Galois sections along torsors
Niels Borne, Michel Emsalem, Jakob Stix
The cuspidalization conjecture, which is a consequence of Grothendieck's section conjecture, asserts that for any smooth hyperbolic curve over a finitely generated field of…
The Nori fundamental gerbe of a fibered category
Niels Borne, Angelo Vistoli
We give a condition that ensures that a fibered category over a field admits a universal morphism to a profinite gerbe. This fundamental gerbe generalizes both Nori's fundamental g…
Parabolic sheaves on logarithmic schemes
Niels Borne, Angelo Vistoli
We show how the natural context for the definition of parabolic sheaves on a scheme is that of logarithmic geometry. The key point is a reformulation of the concept of logarithmic…
Cohomology of G-sheaves in positive characteristic
Niels Borne
Let X be a noetherian scheme defined over an algebraically closed field of positive characteristic p, and G be a finite group, of order divisible by p, acting on X. We introduce a…
A relative Shafarevich theorem
Niels Borne
Suppose given a Galois etale cover Y -> X of proper non-singular curves over an algebraically closed field k of prime characteristic p. Let H be its Galois group, and G any finite…