Towards a specialization map modulo semi-orthogonal decompositions

TL;DR

This paper proposes a conjecture about a specialization map in derived categories of smooth proper varieties, verifies it for specific cases like K3 surfaces and abelian varieties, and explores its implications.

Contribution

It introduces a new conjecture on the existence of a specialization map in derived categories modulo semi-orthogonal decompositions and verifies it for certain classes of varieties.

Findings

Conjecture verified for K3 surfaces.

Conjecture verified for abelian varieties.

Provides a framework for understanding specialization in derived categories.

Abstract

We propose a conjecture on the existence of a specialization map for derived categories of smooth proper varieties modulo semi-orthogonal decompositions, and verify it for K3 surfaces and abelian varieties.