The structure in the nucleus that contains hereditary material is the chromosomes.

Here's a breakdown:

* Nucleus: The control center of the cell, containing the cell's genetic material.

* Chromosomes: Long, thread-like structures made of DNA and proteins. They carry the genetic information (genes) that determine an organism's traits.

* DNA (Deoxyribonucleic acid): The molecule that carries the genetic instructions for an organism's development and function.

So, the chromosomes within the nucleus are responsible for storing and transmitting the hereditary information from one generation to the next.