The contributions in this book explore various contexts in which the derived category of coherent sheaves on a variety determines some of its arithmetic. This setting provides new geometric tools for interpreting elements of the Brauer group. With a view towards future arithmetic applications, the book extends a number of powerful tools for analyzing rational points on elliptic curves, e.g., isogenies among curves, torsion points, modular curves, and the resulting descent techniques, as well as higher-dimensional varieties like K3 surfaces. Inspired by the rapid recent advances in our understanding of K3 surfaces, the book is intended to foster cross-pollination between the fields of complex algebraic geometry and number theory. Contributor...
There has been much interest recently in bounding the Brauer groups of K3 surfaces over number field...
Dans cette thèse, on s’intéresse à des propriétés arithmétiques des variétés algébriques. Elle conti...
We study the distribution of the Brauer group and the frequency of the Brauer-Manin obstruction to t...
This book is motivated by the problem of determining the set of rational points on a variety, but it...
This monograph provides a systematic treatment of the Brauer group of schemes, from the foundational...
This book is devoted to arithmetic geometry with special attention given to the unramified Brauer gr...
The central theme of this book is the study of rational points on algebraic varieties of Fano and in...
Understanding Diophantine equations is one of the fundamental goals of mathematics. Algebraic geomet...
Brauer groups of K3 surfaces behave in many ways like torsion points of elliptic curves. In 1996, M...
In [19], Manin introduced a way to explain the failure of the Hasse principle for algebraic varietie...
We compute the Brauer group of M1;1, the moduli stack of elliptic curves, over Spec ℤ, its localizat...
We compute the Brauer group of M1;1, the moduli stack of elliptic curves, over Spec ℤ, its localizat...
We compute the Brauer group of M1;1, the moduli stack of elliptic curves, over Spec ℤ, its localizat...
We compute the Brauer group of M1;1, the moduli stack of elliptic curves, over Spec ℤ, its localizat...
There has been much interest recently in bounding the Brauer groups of K3 surfaces over number field...
There has been much interest recently in bounding the Brauer groups of K3 surfaces over number field...
Dans cette thèse, on s’intéresse à des propriétés arithmétiques des variétés algébriques. Elle conti...
We study the distribution of the Brauer group and the frequency of the Brauer-Manin obstruction to t...
This book is motivated by the problem of determining the set of rational points on a variety, but it...
This monograph provides a systematic treatment of the Brauer group of schemes, from the foundational...
This book is devoted to arithmetic geometry with special attention given to the unramified Brauer gr...
The central theme of this book is the study of rational points on algebraic varieties of Fano and in...
Understanding Diophantine equations is one of the fundamental goals of mathematics. Algebraic geomet...
Brauer groups of K3 surfaces behave in many ways like torsion points of elliptic curves. In 1996, M...
In [19], Manin introduced a way to explain the failure of the Hasse principle for algebraic varietie...
We compute the Brauer group of M1;1, the moduli stack of elliptic curves, over Spec ℤ, its localizat...
We compute the Brauer group of M1;1, the moduli stack of elliptic curves, over Spec ℤ, its localizat...
We compute the Brauer group of M1;1, the moduli stack of elliptic curves, over Spec ℤ, its localizat...
We compute the Brauer group of M1;1, the moduli stack of elliptic curves, over Spec ℤ, its localizat...
There has been much interest recently in bounding the Brauer groups of K3 surfaces over number field...
There has been much interest recently in bounding the Brauer groups of K3 surfaces over number field...
Dans cette thèse, on s’intéresse à des propriétés arithmétiques des variétés algébriques. Elle conti...
We study the distribution of the Brauer group and the frequency of the Brauer-Manin obstruction to t...