Arshdeep has represented India in 18 ODIs and 91 T20Is so far.
Kishan is currently leading East Zone in the Duleep Trophy.
Sri Lanka made 290 in first innings and were asked to follow on by India.
Prasidh Krishna ripped through Sri Lanka's top-order with a sharp three-wicket spell.
R Ashwin and Cheteshwar Pujara were Indian teammates for over a decade.
Rajat Patidar is only the third captain to back-to-back IPL titles.