October 26, 12:15-13:15, Leiden, Room 411
Jesse Elliott, Generalized Witt Vectors from Profinite Groups I & II
Abstract. Both the ring of "usual" Witt vectors over a commutative ring A relative to a prime p and the ring of "universal" Witt vectors over A are special cases of a more general construction, that of the ring W(G, A) of "generalized" Witt vectors of a profinite group G over A. These special cases correspond respectively to taking G equal to the p-adic and the profinite completion of the additive group of integers. Generally, the ring W(G, A) is a natural quotient of the Grothendieck ring of virtual "A-valued G-sets", which are "almost finite" G-sets equipped with a map to A. In this talk I will present a construction of the ring W(G, A) based on this fact which combines the important elements of two earlier constructions (Dress-Siebeneicher in 1988 and J. Graham in 1993). Fundamental to my construction is a new result concerning W(G, A) which is useful for understanding Witt vectors in general. Prior knowledge of generalized Witt vectors will not be assumed.