No abstract

We compute the cotorsion product of the mod 2 cohomology of spinor group spin(n), which is the E 2 -term of the Rothenberg-Steenrod spectral sequence for the mod 2 cohomology of the classifying space of the spinor group spin(n). As a consequence of this computation, we show the non-collapsing of the Rothenberg-Steenrod spectral sequence for n ≥ 17. 55R40; 55T99

For a fixed prime p, we compute the Brown-Peterson cohomologies of classifying spaces of P U(p) and exceptional Lie groups by using the Adams spectral sequence. In particular, we see that BP * (BP U(p)) and K(n) * (BP U(p)) are even dimensionally generated.

We describe Mùi invariants in terms of Milnor operations and give a simple proof for Mùi's theorem on rings of invariants of polynomial tensor exterior algebras with respect to the action of finite general linear groups. Moreover, we compute some rings of invariants of Weyl groups of maximal non-toral elementary abelian p-subgroups of exceptional Lie groups. 55R40; 55S10

Abstract. We give non-torsion counterexamples against the integral Tate conjecture for finite fields. We extend the result due to Pirutka and Yagita for prime numbers 2, 3, 5 to all prime numbers.