10 citations · 40 across the 18 of their papers we have counts for
18 papers
On Grothendieck's section conjecture for curves of index
Giulio Bresciani
We prove that every hyperbolic curve with a faithful action of a non-cyclic -group (with a few exceptions if ) has a twisted form of index which satisfies Grothendieck'…
The field of moduli of plane curves
Giulio Bresciani
We prove that a smooth, complex plane curve of odd degree can be defined by a polynomial with coefficients in if and only if it is isomorphic to its complex conjugate;…
The field of moduli of varieties with a structure
Giulio Bresciani
If is a variety with an additional structure , such as a marked point, a divisor, a polarization, a group structure and so forth, then it is possible to study whether the pa…
The field of moduli of sets of points in
Giulio Bresciani
For every , we give an example of a finite subset of of degree which does not descend to any Brauer-Severi surface over the field of moduli. Conversely…
The field of moduli of a divisor on a rational curve
Giulio Bresciani
Let be a field with algebraic closure and a reduced, effective divisor of degree , write for the field of moduli…
The arithmetic of tame quotient singularities in dimension
Giulio Bresciani
Let be a field, a variety with tame quotient singularities and a resolution of singularities. Any smooth rational point lifts to by…
An arithmetic valuative criterion for proper maps of tame algebraic stacks
Giulio Bresciani, Angelo Vistoli
The valuative criterion for proper maps of schemes has many applications in arithmetic, e.g. specializing -points to -points. For algebraic stacks,…
Fields of moduli and the arithmetic of tame quotient singularities
Giulio Bresciani, Angelo Vistoli
Given a perfect field with algebraic closure and a variety over , the field of moduli of is the subfield of of elements fixe…
The genericity theorem for the essential dimension of tame stacks
Giulio Bresciani, Angelo Vistoli
Let be a regular tame stack. If is locally of finite type over a field, we prove that the essential dimension of is equal to its generic essential dimension, this gener…
On the birational section conjecture with strong birationality assumptions
Giulio Bresciani
Let be a curve over a field finitely generated over and an indeterminate. We prove that, if is a section of such tha…
On the section conjecture and Brauer-Severi varieties
Giulio Bresciani
J. Stix proved that a curve of positive genus over which maps to a non-trivial Brauer-Severi variety satisfies the section conjecture. We prove that, if is a curve…
A higher dimensional Hilbert irreducibility theorem
Giulio Bresciani
Assuming the weak Bombieri-Lang conjecture, we prove that a generalization of Hilbert's irreducibility theorem holds for families of geometrically mordellic varieties (for instance…
An elementary approach to Stix's proof of the real section conjecture
Giulio Bresciani, Angelo Vistoli
We give an elementary proof of the real section conjecture for quasi-projective hyperbolic curves and semi-abelian varieties. The underlying argument is essentially equivalent to t…
On the Bombieri-Lang Conjecture over finitely generated fields
Giulio Bresciani
The strong Bombieri-Lang conjecture postulates that, for every variety of general type over a field finitely generated over , there exists an open subset $U\sub…
On the section conjecture over fields of finite type
Giulio Bresciani
Assume that the section conjecture holds over number fields. We prove then that it holds for a broad class of curves defined over finitely generated extensions of . Thi…
Essential dimension and pro-finite group schemes
Giulio Bresciani
A. Vistoli observed that, if Grothendieck's section conjecture is true and is a smooth hyperbolic curve over a field finitely generated over , then $\underlineπ_{1}…
Some implications between Grothendieck's anabelian conjectures
Giulio Bresciani
Grothendieck gave two forms of his "main conjecture of anabelian geometry", i.e. the section conjecture and the hom conjecture. He stated that these two forms are equivalent and th…
On Grothendieck's section conjecture for orbicurves
Giulio Bresciani
As already noted by Niels Borne and Michel Emsalem, there is a natural generalization of the section conjecture for proper orbicurves. Combined with the reformulation by Niels Born…