Generalized non-commutative degeneration conjecture

TL;DR

This paper proposes a broad generalization of the Kontsevich--Soibelman degeneration conjecture, extending it to arbitrary small DG categories and linking it to other conjectures in the field.

Contribution

It introduces a new generalized conjecture on the degeneration of Hochschild-to-cyclic spectral sequences for DG categories, building on existing conjectures.

Findings

The generalized conjecture follows from the original Kontsevich--Soibelman conjecture.

It connects the degeneration conjecture to the conjecture on smooth categorical compactification.

Provides a framework for understanding spectral sequence degeneration in a broader categorical context.

Abstract

In this paper we propose a generalization of the Kontsevich--Soibelman conjecture on the degeneration of Hochschild-to-cyclic spectral sequence for smooth and compact DG category. Our conjecture states identical vanishing of a certain map between bi-additive invariants of arbitrary small DG categories over a field of characteristic zero. We show that this generalized conjecture follows from the Kontsevich--Soibelman conjecture and the so--called conjecture on smooth categorical compactification.