Evaluating the tame Brauer group of open varieties over local fields
Victor de Vries

TL;DR
This paper investigates the evaluation map of the Brauer group on open varieties over local fields, establishing conditions under which evaluations at different points coincide, with implications for understanding the tame Brauer group.
Contribution
It provides new criteria for when evaluation maps of the Brauer group are equal for points lifting to the same reduction and intersection class in a regular scheme over local fields.
Findings
Evaluation maps coincide under specific reduction and intersection conditions.
Conditions relate to the reduction of points and their intersection classes in the divisor.
Results enhance understanding of the tame Brauer group over local fields.
Abstract
In this document we let be a smooth variety of pure dimension over a local field with unit ball and residue field of characteristic and we set to be a positive integer such that . For various we study the evaluation map . We suppose that embeds as an open subscheme in a regular scheme that is of finite type over . We assume that is a divisor and we endow it with its reduced scheme structure. We show that for that lift to we obtain the same evaluation map under the two conditions that first, there is an equality of reductions in and second, that $\mathrm{cl}(x_1\cap…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Advanced Algebra and Geometry
