Universal Koszulity conjecture for Galois cohomology

About 8 years old · traced to

Let pp be prime, let FF be a field containing a primitive ppth root of unity, and assume that GF(p)G_F(p) is finitely generated. Write H∙(GF(p),Fp)H^\bullet(G_F(p),\mathbb{F}_p) for the continuous cohomology algebra. An algebra is universally Koszul when every ideal generated by degree-11 elements, equivalently every cyclic module of the relevant form, has a linear resolution. Universal Koszulity conjecture. The algebra

H∙(GF(p),Fp)H^\bullet(G_F(p),\mathbb{F}_p)

is universally Koszul. The paper presents this as a strengthening of the quadraticity supplied by Bloch–Kato; it is proved conditionally under the Elementary Type Conjecture, while the unconditional general case remains open.

References

Primary source

Jan Minac, Marina Palaisti, Federico W. Pasini and Nguyen Duy Tan, “Enhanced Koszul properties in Galois cohomology”, arXiv:1811.09272 (2020).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.