Im' working on the book of Lang "introduction to arakelov theory".
In the 4th chapter "Hodge index and adjunction formula" p. 99 Lang gives the following :
Let $X$ be an arithmetic surface over the ring of integers of a number field, and let $E$ an horizontal curve over X.
I have been looking for the definition of a curve on an artihmetic surface since this morning. Is it just a divisor? Because i know what's a horizontal divisor !
Thanks for help !