59 research outputs found
Cohomological Hasse principle and motivic cohomology for arithmetic schemes
In 1985 Kazuya Kato formulated a fascinating framework of conjectures which
generalizes the Hasse principle for the Brauer group of a global field to the
so-called cohomological Hasse principle for an arithmetic scheme. In this paper
we prove the prime-to-characteristic part of the cohomological Hasse principle.
We also explain its implications on finiteness of motivic cohomology and
special values of zeta functions.Comment: 47 pages, final versio
Concentration or representation : the struggle for popular sovereignty
There is a tension in the notion of popular sovereignty, and the notion of democracy associated with it, that is both older than our terms for these notions themselves and more fundamental than the apparently consensual way we tend to use them today. After a review of the competing conceptions of 'the people' that underlie two very different understandings of democracy, this article will defend what might be called a 'neo-Jacobin' commitment to popular sovereignty, understood as the formulation and imposition of a shared political will. A people's egalitarian capacity to concentrate both its collective intelligence and force, from this perspective, takes priority over concerns about how best to represent the full variety of positions and interests that differentiate and divide a community
Campana points of bounded height on vector group compactifications
We initiate a systematic quantitative study of subsets of rational points
that are integral with respect to a weighted boundary divisor on Fano
orbifolds. We call the points in these sets Campana points. Earlier work of
Campana and subsequently Abramovich shows that there are several reasonable
competing definitions for Campana points. We use a version that delineates well
different types of behaviour of points as the weights on the boundary divisor
vary. This prompts a Manin-type conjecture on Fano orbifolds for sets of
Campana points that satisfy a klt (Kawamata log terminal) condition. By
importing work of Chambert-Loir and Tschinkel to our set-up, we prove a log
version of Manin's conjecture for klt Campana points on equivariant
compactifications of vector groups.Comment: 52 pages; minor revision, changes in the definition of Campana point
- …