Counting Semilinear Endomorphisms Over Finite Fields

Mathematics – Algebraic Geometry

Scientific paper

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Scientific paper

For a finite field k and a triple of integers g \ge r \ge s \ge 0, we count
the number of semilinear endomorphisms of a g-dimensional k-vector space which
have rank r and stable rank s. Such endomorphisms show up naturally in the
classification of finite flat group schemes of p-power order over k which are
killed by p and have p-rank s, via Dieudonne theory.

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