On certain arithmetical invariants of Fermat varieties (Q1076098)

Let \(q=p^ f\), where \(p\) is a prime. Let \(X(r,m)\) be the Fermat variety of dimension \(r\) and degree \(m\) defined over \(\mathbb F_ q\). Fix \(m\). Then the author proves that certain arithmetical invariants of \(X(r,m)\) depend only on the class of \(p\) modulo \(m\). These invariants include the stable rank and Picard number of the variety. Generalizations to products and quotients of Fermat varieties are also given.