English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Making use of noncommutative motives we relate exceptional collections (andmore generally semi-orthogonal decompositions) to motivic decompositions. Onone hand we prove that the Chow motive M(X) of every smooth properDeligne-Mumford stack X, whose bounded derived category D(X) of coherentschemes admits a full exceptional collection, decomposes into a direct sum oftensor powers of the Lefschetz motive. Examples include projective spaces,quadrics, toric varieties, homogeneous spaces, Fano threefolds, and modulispaces. On the other hand we prove that if M(X) decomposes into a direct sum oftensor powers of the Lefschetz motive and moreover D(X) admits asemi-orthogonal decomposition, then the noncommutative motive of each one ofthe pieces of the semi-orthogonal decomposition is a direct sum of the tensorunit. As an application we obtain a simplification of Dubrovin's conjecture.

From exceptional collections to motivic decompositions via noncommutative motives