Arkiv för Matematik

Volume 59 (2021)

Number 2

A Riemann–Roch type theorem for twisted fibrations of moment graphs

Pages: 359 – 384



Martina Lanini (Dipartimento di Matematica, Università degli di Roma “Tor Vergata”, Rome, Italy)

Kirill Zainoulline (Department of Mathematics and Statistics, University of Ottawa, Ontario, Canada)


In the present paper we extend the Riemann–Roch formalism to structure algebras of moment graphs. We introduce and study the Chern character and push-forwards for twisted fibrations of moment graphs. We prove an analogue of the Riemann–Roch theorem for moment graphs. As an application, we obtain the Riemann–Roch type theorem for the equivariant $K$‑theory of some Kac–Moody flag varieties.


equivariant cohomology, Chern character, Riemann–Roch theorem, moment graph, structure algebra

2010 Mathematics Subject Classification

14F05, 14F43, 14M15

Received 28 March 2021

Received revised 22 April 2021

Accepted 3 May 2021

Published 11 November 2021