### p-adic Arakelov theory, by Amnon Besser

We introduce the p-adic analogue of Arakelov intersection theory on
arithmetic surfaces. The intersection pairing in an extension of the p-adic
height pairing for divisors of degree 0 in the form described by Coleman and
Gross. It also uses Coleman integration and is related to work of Colmez on
p-adic Green functions. We introduce the p-adic version of a metrized line
bundle and define the metric on the determinant of its cohomology in the
style of Faltings. It is possible to prove in this theory analogues of the
Adjunction formula and the Riemann-Roch formula.

Amnon Besser <bessera@math.bgu.ac.il>