Bryant G. Mathews: Canonical dimension of projective PGL_1(A)-homogeneous varieties

Submission: 2009, Mar 30

Let A be a central division algebra over a field F with ind A = n. In computing canonical p-dimension of projective PGL_1(A)-homogeneous varieties, for p prime, we can reduce to the case of generalized Severi-Brauer varieties X_e(A) with ind A a power of p divisible by e. We prove that canonical 2-dimension (and hence canonical dimension) equals dimension for all X_e(A) with ind A = 2e a power of 2.

2000 Mathematics Subject Classification: 20G15; 14C25

Keywords and Phrases: canonical dimension, incompressibility, projective homogeneous varieties, generalized Severi-Brauer varieties

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