LARGE intersection_pairing.jpg (The intersection pairing. Loic computes the intersection pairing on special elements of homology by reducing it to the case of plaine curve. He then observes that the computation extends to all elements using the first "Bernoulli polynomial". ) |
LARGE manin_reciprocity.jpg (Manin reciprocity is something that looks like quadratic reciprocity and follows from the description of Hecke operators in terms of Manin symbols. According to Merel, this observation made Mazur and others quite excited in the 1970s. ) |
LARGE modsym_isom.jpg (Reduction to weight 2 in characteristic p at the expense of increasing the level.) |