Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	阮洋洋，北京师范大学
Inviter:
Title:	Cohomology of classifying spaces of rank 3 Kac-Moody groups
Time & Venue:	2021.01.07 14:00-16:00 晨兴中心510室
Abstract:	My talk has two parts: 1.Cohomology of classifying spaces of rank 3 Kac-Moodygroups I will introduce a method to compute the rational and mod p cohomology groups of classifying space of rank 3 Kac-Moody group with infinite Weyl group, and represent these cohomology groups by sum and quotient of the invariants of Weyl group and its subgroups. Using these results, we find that for any prime p,there are p-torsion elements in the integral cohomology groups of classifying spaces of rank 3 Kac-Moody groups with infinite Weyl group. 2.The computation of Balmer spectrum of the G-equivariant stable homotopy category Asin a commutative ring,for a finite group G, Balmer defined the “prime ideal” in G-equivariant stable homotopy category SH(G)with its tensor-triangular structure. All “prime ideals” with “Zariski topology” form the Balmer spectrum Spec(SH(G)^c). The computation of Balmer spectrum is very important to understand G-equivariant stable homotopy category. To determine the “Zariski topology” on Spec(SH(G)^c), it suffices to determine the inclusion relations for these “prime ideals”. In 2017,Balmer and Sanders determined the Balmer spectrum Spec(SH(Z/p)^c). And in 2019, Barthel, Hausmann, Naumann, Nikolaus, Noel, and Stapleton determined the Balmer spectrum Spec(SH(G)^c) for arbitrary finite abelian group. I will give a newmethod to finish the computation, which is more elementary and conceptual.