---
abstract: 'We propose an analogue of Dubrovin’s conjecture for the case where Fano manifolds have quantum connections of exponential type. It includes the case where the quantum cohomology rings are not necessarily semisimple. The conjecture is described as an isomorphism of two linear algebraic structures, which we call \`\`mutation systems". Given such a Fano manifold $X$, one of the structures is given by the Stokes structure of the quantum connection of $X$, and the other is given by a semiorthogonal decomposition of the derived category of coherent sheaves on $X$. We also prove the conjecture for a class of smooth Fano complete intersections in a projective space.'
author:
- 'Fumihiko Sanda, Yota Shamoto'
bibliography:
- 'dubrovin.bib'
title: 'An analogue of Dubrovin’s conjecture'
---

Introduction
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The purpose of this paper is to propose an analogue of Dubrovin’s conjecture [@dubgeo] in a more general setting. We shall firstly recall the original conjecture of Dubrovin in §\[intro dub\]. We also review Gamma conjecture of Galkin-Golyshev-Iritani [@ggi], [@gi] in §\[intro gamma\] since their result plays a key role in this paper. Then we explain the outline of the formulation and the main result in §\[intro mutation system\]-§\[intro main theorem\].

Dubrovin’s conjecture {#intro 