Symmetric powers of Galois modules on Dedekind schemes

Dedekind 整环上一般线性群的同调稳定性

Homological stability for general linear groups over Dedekind domains

该研究针对 Dedekind 整环上有限生成投射模的自同构群，提出了考虑所有稳定化映射的新型同调稳定性定理，并验证了约化 Borel--Serre 空间也具备该稳定性。

Galois module structure of Galois cohomology for embeddable cyclic extensions of degree p^n

Let p>2 be prime, and let n,m be positive integers. For cyclic field extensions E/F of degree p^n that contain a primitive pth root of unity, we show that the associated F_p[Gal(E/F)]-modules H^m(G_E,mu_p) have a sparse decomposition. When E/F is additionally a subextension of a cyclic, degree p^{n+1} extension E'/F, we give a more refined F_p[Gal(E/F)]-decomposition of H^m(G_E,mu_p).

Galois module structure of Milnor K-theory mod p^s in characteristic p

Let E be a cyclic extension of pth-power degree of a field F of characteristic p. For all m, s in N, we determine K_mE/p^sK_mE as a (Z/p^sZ)[Gal(E/F)]-module. We also provide examples of extensions for which all of the possible nonzero summands in the decomposition are indeed nonzero.

Galois module structure of Galois cohomology and partial Euler-Poincare characteristics

Let F be a field containing a primitive pth root of unity, and let U be an open normal subgroup of index p of the absolute Galois group G_F of F. Using the Bloch-Kato Conjecture we determine the structure of the cohomology group H^n(U,Fp) as an Fp[G_F/U]-module for all n in N. Previously this structure was known only for n=1, and until recently the structure even of H^1(U,Fp) was determined only for F a local field, a case settled by Borevic and Faddeev in the 1960s. We apply these results to study partial Euler-Poincare characteristics of open subgroups N of the maximal pro-p quotient T of G_…

群在交叉模系数下的非阿贝尔上同调与伽罗瓦上同调

Non-abelian hypercohomology of a group with coefficients in a crossed module, and Galois cohomology

发展了群在交叉模系数下的上同调理论，并应用于定义约化代数群伽罗瓦上同调的阿贝尔化映射。

Equivariant Hopf Galois extensions and Hopf cyclic cohomology

We define the notion of equivariant Hopf Galois extension and apply it as a functor between category of SAYD modules of the Hopf algebras involving in the extension. This generalizes the result of Jara-Stefan and Böhm-Stefan on associating a SAYD modules to any ordinary Hopf Galois extension.