Let Γ denote a group of finite virtual cohomological dimension and p a prime. If the cohomology ring H∗(Γ;Fp) has Krull dimension one, the p-period of Γ is defined; it measures the periodicity of H∗(Γ;Fp) in degrees above the virtual cohomological dimension of Γ. The Yagita invariant p(Γ) of Γ is a natural generalization of the p-period to groups with H∗(Γ;Fp) of Krull dimension larger than one...

of the Dissertation Affine Stratifications and equivariant vector bundles on the moduli of principally polarized abelian varieties by Anant Atyam Doctor of Philosophy in Mathematics Stony Brook University 2014 We explicitly construct a locally closed affine stratification of the coarse moduli space of principally polarized complex abelian four folds A4 and using [32], produce an upper bound for...

Fields of cohomological dimension one versus C 1-fields J.-L. Colliot-Théì ene Summary. Ax gave examples of fields of cohomological dimension 1 which are not C 1-fields. Kato and Kuzumaki asked whether a weak form of the C 1-property holds for all fields of cohomological dimension 1 (existence of solutions in extensions of coprime degree rather than existence of a solution in the ground field)....