Period and Index in the Brauer Group of an Arithmetic Surface
نویسنده
چکیده
This paper consists of two parts: in the first, we use the deformation theory of twisted sheaves on stacks to generalize results of de Jong and Saltman on the period-index problem for the Brauer group, yielding various new cases of the standard conjecture. In the second part, we use the geometric techniques of the first part to relate the Hasse principle for certain smooth projective geometrically rational varieties over global fields to the period-index problem for Brauer groups of arithmetic surfaces. We also include an appendix by D. Krashen showing that the period-index bounds of the first part are
منابع مشابه
Brauer groups on K 3 surfaces and arithmetic applications
For a prime p, we study subgroups of order p of the Brauer group Br(S) of a general complex polarized K3 surface of degree 2d, generalizing earlier work of van Geemen. These groups correspond to sublattices of index p of the transcendental lattice TS of S; we classify these lattices up to isomorphism using Nikulin’s discriminant form technique. We then study geometric realizations of p-torsion ...
متن کامل2 2 A pr 2 01 4 Brauer groups on K 3 surfaces and arithmetic applications ∗
For a prime p, we study subgroups of order p of the Brauer group Br(S) of a general complex polarized K3 surface of degree 2d, generalizing earlier work of van Geemen. These groups correspond to sublattices of index p of the transcendental lattice TS of S; we classify these lattices up to isomorphism using Nikulin’s discriminant form technique. We then study geometric realizations of p-torsion ...
متن کاملArithmetic Aspects of Moduli Spaces of Sheaves on Curves
We describe recent work on the arithmetic properties of moduli spaces of stable vector bundles and stable parabolic bundles on a curve over a global field. In particular, we describe a connection between the period-index problem for Brauer classes over the function field of the curve and the Hasse principle for rational points on étale forms of such moduli spaces, refining classical results of ...
متن کاملStanford Algebraic Geometry — Seminar — MODULI OF TWISTED SHEAVES AND AZUMAYA ALGEBRAS
We construct and describe moduli spaces of Azumaya algebras on a smooth projective surface. These spaces are the algebro-geometric version of the spaces of principal PGL n -bundles and they also have strong connections to arithmetic. A geometric approach to the problem leads one to study moduli spaces of twisted sheaves. We show that these spaces are very similar to the moduli spaces of semi-st...
متن کاملA Note on the First Geometric-Arithmetic Index of Hexagonal Systems and Phenylenes
The first geometric-arithmetic index was introduced in the chemical theory as the summation of 2 du dv /(du dv ) overall edges of the graph, where du stand for the degree of the vertex u. In this paper we give the expressions for computing the first geometric-arithmetic index of hexagonal systems and phenylenes and present new method for describing hexagonal system by corresponding a simple g...
متن کامل