Iwasawa theory of automorphic representations of GL2n at non-ordinary primes

Let Pi be a cuspidal automorphic representation of GL(2n)(A(Q)), and let p be an odd prime at which Pi is unramified. In a recent work, Barrera, Dimitrov and Williams constructed possibly unbounded p-adic L-functions interpolating complex L-values of Pi in the non-ordinary case. Under certain assumptions, we construct two bounded p-adic L-functions for Pi, thus extending an earlier work of Rockwood by relaxing the Pollack condition. Using Langlands local-global compatibility, we define signed Selmer groups over the p-adic cyclotomic extension of Q attached to the p-adic Galois representation of Pi and formulate Iwasawa main conjectures in the spirit of Kobayashi's plus and minus main conjectures for p-supersingular elliptic curves.