26 citations · 46 across the 10 of their papers we have counts for
12 papers
A note on complex Lie Algebras isomorphic to their conjugate
Cyril Demarche
A real Lie algebra defines by extension of scalars a complex Lie algebra that is isomorphic to its Galois conjugate. In this paper, we are interested in the converse property: give…
Degree 4 cohomological invariants of algebraic tori
Cyril Demarche, Hanqing Long
In this paper, we determine the motive of the classifying torsor of an algebraic torus. As a result, we give an exact sequence describing the degree 4 cohomological invariants of a…
Lifting Galois representations via Kummer flags
Andrea Conti, Cyril Demarche, Mathieu Florence
Let be either i) the absolute Galois group of a local field , or ii) the topological fundamental group of a closed connected orientable surface of genus . In case i), ass…
Local-global principles for homogeneous spaces of reductive groups over global function fields
Cyril Demarche, David Harari
Let be a global field of positive characteristic. We prove that the Brauer-Manin obstructions to the Hasse principle, to weak approximation and to strong approximation are the…
Duality for complexes of tori over a global field of positive characteristic
Cyril Demarche, David Harari
If K is a number field, arithmetic duality theorems for tori and complexes of tori over K are crucial to understand local-global principles for linear algebraic groups over K. When…
Artin-Mazur-Milne duality for fppf cohomology
Cyril Demarche, David Harari
We provide a complete proof of a duality theorem for the fppf cohomology of either a curve over a finite field or a ring of integers of a number field, which extends the classical…
Splitting families in Galois cohomology
Cyril Demarche, Mathieu Florence
Let be a field, with absolute Galois group . Let be a finite étale group scheme of multiplicative type, i.e. a discrete -module. Let be an integer, and l…
Étale homotopy groups of algebraic groups and homogeneous spaces
Cyril Demarche, Tamás Szamuely
We show the vanishing of the second homotopy group of the étale homotopy type of a smooth connected algebraic group over a separably closed field, completed away from the character…
Comparing descent obstruction and Brauer-Manin obstruction for open varieties
Yang Cao, Cyril Demarche, Fei Xu
We provide a relation between Brauer-Manin obstruction and descent obstruction for torsors over open varieties under a connected linear algebraic group or a group of multiplicative…
The Grunwald problem and approximation properties for homogeneous spaces
Cyril Demarche, Giancarlo Lucchini Arteche, Danny Neftin
Given a group and a number field , the Grunwald problem asks whether given field extensions of completions of at finitely many places can be approximated by a single fie…
Hasse principle and weak approximation for multinorm equations
Cyril Demarche, Dasheng Wei
In this note, we are interested in local-global principles for multinorm equations of the form where is a global field, are finite s…
Manin obstruction to strong approximation for homogeneous spaces
Mikhail Borovoi, Cyril Demarche
For a homogeneous space X (not necessarily principal) of a connected algebraic group G (not necessarily linear) over a number field k, we prove a theorem of strong approximation fo…