Date: September 16,18,20,23,25,27 

Time: 13:00-15:00

The course will have two parts. In the first part X is a projective regular scheme over Z of Kull dimension d, and  L1,...,Ld are d hermitian line bundles on X. By induction on d, we define a real number L1∙L2∙...∙Ld,, which is equal to heights in some cases. In the second part d=2. Let ω be the relative dualizing sheaf on X, endowed with its Arakelov metric. Parshin and Moret-Bailly expect the number ω·ω to be bounded from above. We present this conjecture, and its link to ABC.