Comparison of the two notions of characteristic cycles

Ankit Rai

Journal of Singularities
volume 28 (2025), 39-54

Received: 22 March 2024. In revised form: 19 December 2024

DOI: 10.5427/jsing.2025.28c


Abstract:

Given a constructible sheaf F on a complex manifold, Kashiwara-Schapira defined the notion of singular support and characteristic cycle of F. On the other hand for a Zariski constructible étale sheaf F on an algebraic variety X, Beilinson defined the notion of singular support of F and Saito defined the notion of characteristic cycle of F. In this article we compare these notions and prove that they agree in a suitable sense. In the appendix we discuss extension of the notions of singular support and characteristic cycles developed by Umezaki-Yang-Zhao and Barrett.

Ankit Rai, Chennai Mathematical Institute, H1, SIPCOT IT Park, Siruseri, Kelambakkam 603103, India} \email{ankitr@cmi.ac.in}


Author(s) information:

Ankit Rai
Chennai Mathematical Institute
H1, SIPCOT IT Park
Siruseri, Kelambakkam 603103, India
email: ankitr@cmi.ac.in