Gabriel Dill

In joint work in progress with Francesco Campagna, we formulate a conjecture about unlikely intersections in split semiabelian schemes over some ring of $S$-integers in a number field. Broadly speaking, if an intersection with a subgroup scheme is unlikely for dimension reasons, its "size" should not be too big compared to the "complexity" of the subgroup scheme. Focusing on the case of powers of the multiplicative group over the rational integers, I will show some evidence that we have acquired so far for our conjecture and discuss in some detail the example of a certain arithmetic surface inside the fibered cube of the multiplicative group over the integers, which leads to the sequence of integers from the title.