We study the Brauer classes rising from the obstruction to the existence of tautological line bundles on the Picard scheme of curves. We establish various properties of the Brauer classes for families of smooth curves. We compute the period and index of the Brauer class associated with the universal smooth curve for a fixed genus. We also show such Brauer classes are trivialized when we specialize to certain generalized theta divisors. If we consider the universal totally degenerate curve with a fixed dual graph, using symmetries of the graph, we give bounds on the period and index of the Brauer classes. As a result, we provide some division algebras of prime degree, serving as candidates for the cyclicity problem. As a byproduct, we re-calculate the period and index of the Brauer class for universal smooth genus g curve in an elementary way. We study certain conic associated with the universal totally degenerate curve with a fixed dual graph. We show the associated conic is non-split in some cases. We also study some other related geometric properties of Brauer groups.

Thesis supervisor: Frederick M. Goodman. Includes bibliographic references (p. 84-88).

Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references. Available also from UMI/Dissertation Abstracts International.

Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references (leaves 106-107). Available also in a digital version from Dissertation Abstracts.

Not available / text

This thesis is concerned with the Regular Inverse Galois Problem for p-groups over fields of characteristic unequal to p. Building upon results of Saltman, Dentzer characterized a class of finite groups that are automatically realized over every field, and proceeded to show that every group of order dividing p⁴ belongs to this class. We extend this result to include groups of order p⁵, provided that the base field k contains the p³-th roots of unity. The proof involves reducing to certain Brauer embedding problems defined over the rational function field k(x). Through explicit computation, we describe the cohomological obstructions to these embedding problems. Then by applying results about the Brauer group of a Dedekind domain, we show that they all possess solutions. / text

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.