The standardness conjecture for prime ideals in solvable uniform Iwasawa algebras
The standardness conjecture for prime ideals in solvable uniform Iwasawa algebras
Let be a prime, let be a finite extension of with ring of integers , and let be a compact -adic Lie group. Its completed group algebra is
where ranges over the open normal subgroups of . A prime ideal of is standard if there is a closed normal subgroup of such that, writing , the group is torsionfree, , and the image of in is centrally generated. It is virtually standard if is a finite intersection of standard prime ideals of for some open normal subgroup of .
The standardness conjecture. Let be a solvable, uniform pro- group, and let be a prime ideal in . Then is virtually standard, and moreover if then is standard.
This conjecture seeks to reduce all prime ideals in solvable uniform Iwasawa algebras to augmentation ideals and centrally generated ideals. The supplied text gives no evidence that the conjecture has been resolved.
Sources & referencesView supporting material
Primary source
Adam Jones, “Primitive ideals in rational, nilpotent Iwasawa algebras”, arXiv:2102.04165 (2021).
Progress summary
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