**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.