Non-communtative Iwasawa main conjecture - Witte, Malte (International journal of number theory, 2020)
We formulate and prove an analogue of the non-commutative Iwasawa Main Conjecture for l-adic representations of the Galois group of a function field of characteristic p. We also prove a functional equation for the resulting non-commutative L-functions. As corollaries, we obtain non-commutative generalizations of the main conjecture for Picard-1-motives of Greither and Popescu and a main conjecture for abelian varieties over function fields in precise analogy to the GL(2) main conjecture of Coates, Fukaya, Kato, Sujatha and Venjakob.
Gesehen am 09.11.2020