Constant Terms of Coleman Power Series And Euler Systems in Function Field

Abstract

We calculate the constant term of Coleman power series and use it to prove an analogue of Iwasawa Main Conjecture in function fields of characteristic p>0 using Euler systems. This result is proved by a similar method of classical proof of Iwasawa Main Conjecture, go back to Kolyvagin and Rubin. We construct Euler systems from theta function of Drinfeld modules and establish finite-singular comparison equation even when p is not invertible the coefficients.