26 citations · 65 across the 18 of their papers we have counts for
19 papers · 1 filter
Stack of -covers
Fabio Tonini
The aim of this paper is to study the geometry of the stack of -covers. We show that it has two irreducible components and meeting in…
Drinfeld-Lau Descent over Fibered Categories
Valentina Di Proietto, Fabio Tonini, Lei Zhang
Let be a category fibered in groupoids over a finite field , and let be an algebraically closed field containing . Denote by $ϕ_k\col…
Stacks of fiber functors and Tannaka's reconstruction
Fabio Tonini
Given a quasi-compact category fibered in groupoids and a monoidal subcategory of its category of locally free sheaves , we ar…
Cox rings of algebraic stacks
Andreas Hochenegger, Elena Martinengo, Fabio Tonini
We give a proper definition of the multiplicative structure of the following rings: the Cox ring of invertible sheaves on a general algebraic stack; and the Cox ring of rank one re…
A generalized Abhyankar's conjecture for simple Lie algebras in characteristic
Shusuke Otabe, Fabio Tonini, Lei Zhang
In the present paper, we study a purely inseparable counterpart of Abhyankar's conjecture for the affine line in positive characteristic, and prove its validity for all the finite…
Moduli of formal torsors II
Fabio Tonini, Takehiko Yasuda
Applying the authors' preceding work, we construct a version of the moduli space of -torsors over the formal punctured disk for a finite group . To do so, we introduce two Gr…
Notes on the motivic McKay correspondence for the group scheme
Fabio Tonini, Takehiko Yasuda
We formulate a conjecture on the motivic McKay correspondence for the group scheme in characteristic and give a few evidences. The conjecture especially claims that…
The arithmetic local Nori fundamental group
M. Romagny, F. Tonini, L. Zhang
In this paper we introduce the local Nori fundamental group scheme of a reduced scheme or algebraic stack over a perfect field . We give particular attention to the case of fiel…
Moduli of formal torsors
Fabio Tonini, Takehiko Yasuda
We construct the moduli stack of torsors over the formal punctured disk in characteristic p > 0 for a finite group isomorphic to the semidirect product of a p-group and a tame cycl…
Nori fundamental gerbe of essentially finite covers and Galois closure of towers of torsors
M. Antei, I. Biswas, M. Emsalem +2
We prove the existence of a Galois closure for towers of torsors under finite group schemes over a proper, geometrically connected and geometrically reduced algebraic stack ove…
Essentially Finite Vector Bundles on Normal Pseudo-proper Algebraic Stacks
Fabio Tonini, Lei Zhang
Let be a normal, connected and projective variety over an algebraically closed field . It is known that a vector bundle on is essentially finite if and only if it is…
-divided sheaves trivialized by dominant maps are essentially finite
Fabio Tonini, Lei Zhang
By a result of Biswas and Dos Santos, on a smooth and projective variety over an algebraically closed field, a vector bundle trivialized by a proper and surjective map is essential…
Algebraic and Nori fundamental gerbes
Fabio Tonini, Lei Zhang
In this paper we extend the generalized algebraic fundamental group constructed by Esnault and Hogadi to general fibered categories using the language of gerbes. As an application…
Ramified Galois covers via monoidal functors
Fabio Tonini
We interpret Galois covers in terms of particular monoidal functors, extending the correspondence between torsors and fiber functors. As applications we characterize tame -cover…
Sheafification of linear functors
Fabio Tonini
We introduce ``sheafification'' functors from categories of (lax monoidal) linear functors to categories of quasi-coherent sheaves (of algebras) of stacks. They generalize the homo…
Stacks of uniform cyclic covers of curves and their Picard groups
Flavia Poma, Mattia Talpo, Fabio Tonini
We study the stack B_{h,g,n} of uniform cyclic covers of degree n between smooth curves of genus h and g and, for h >> g, present it as an open substack of a vector bundle over the…
Stacks of ramified Galois covers
Fabio Tonini
Given a finite, flat and finitely presented group scheme over some base , we introduce the notion of ramified -covers and study the moduli stack -Cov they form. The th…
Stacks of ramified abelian covers
Fabio Tonini
Given a flat, finite group scheme G finitely presented over a base scheme we introduce the notion of ramified Galois cover of group G (or simply G-cover), which generalizes the not…
ACM bundles on del Pezzo surfaces
Joan Pons-Llopis, Fabio Tonini
ACM rank 1 bundles on del Pezzo surfaces are classified in terms of the rational normal curves that they contain. A complete list of ACM line bundles is provided. Moreover, for any…