SCIENTIFIC PROGRAMS AND ACTIVITIES
|August 23, 2017|
The goal of this series of lecture is to present the theory of
the Eisenstein ideal for proving one divisibility towards the so-
The student project will be on writting a detailed account on one of the steps of the arguments presented in the lectures. A particularly important point is to determined the relation between the type (the local conditions at primes dividing p) of the Selmer group considered in relation with the signature of the unitary group from which the Eisentein ideal is defined. In the lecture series, we will focus on the U(2,2) and U(3,1) cases. The student project would be for instance to figure out what is happening in the more general U(p,q)-situation. Another important step in this strategy is the construction of some universal lattice. I will only sketch the proof during the lecture. One project could be to write a complete proof of the construction and the main properties of this lattice.