Selmer ranks for some fourdimensional symplectic Galois representations, in the spirit of bipartite Euler systems
Selmer ranks for some fourdimensional symplectic Galois representations, in the spirit of bipartite Euler systems

Naomi Sweeting, Princeton University
Fine Hall 224
I will describe a new bipartite Euler systemtype construction system for GSp_4 and its inner forms, based on the special cycles appearing in the Kudla program (for instance, Shimura curves on Siegel threefolds). This leads to new results towards the BlochKato Conjectures in ranks 0 and 1 for fourdimensional Galois representations associated to Siegel modular forms of parallel weights (3,3). The key ingredients of the proof are the structure of the supersingular locus for special fibers of GSpin_5 Shimura varieties at primes of both good and bad reduction, along with the representation theory of theta lifts underlying Kudla's program.