Weil restriction of noncommutative motives

Research output: Contribution to journalArticlepeer-review

Abstract

The Well restriction functor, introduced in the late fifties, was recently extended by Karpenko to the category of Chow motives with integer coefficients. In this article we introduce the noncommutative (= NC) analogue of the Weil restriction functor, where schemes are replaced by dg algebras, and extend it to Kontsevich's categories of NC Chow motives and NC numerical motives. Instead of integer coefficients, we work more generally with coefficients in a binomial ring. Along the way, we extend Karpenko's functor to the classical category of numerical motives, and compare this extension with its NC analogue. As an application, we compute the (NC) Chow motive of the Well restriction of every smooth projective scheme whose category of perfect complexes admits a full exceptional collection. Finally, in the case of central simple algebras, we describe explicitly the NC analogue of the Weil restriction functor using solely the degree of the field extension. This leads to a "categorification" of the classical corestriction homomorphism between Brauer groups.
Original languageEnglish
Pages (from-to)119-152
JournalJournal of Algebra
Volume430
DOIs
Publication statusPublished - 2015

Keywords

  • (Noncommutative) pure motives
  • Binomial ring
  • Central simple algebra
  • Full exceptional collection
  • Galois descent
  • Noncommutative algebraic geometry
  • Weil restriction

Fingerprint

Dive into the research topics of 'Weil restriction of noncommutative motives'. Together they form a unique fingerprint.

Cite this