Algebra Seminar, Andrew Schultz (Wellesley): 'Parameterizing solutions to Galois embedding problems via modules'

Friday, April 10, 2015
1:10 PM - 2:00 PM (ET)
ESC 638
Event Type
Academic Calendar
Christopher Rasmussen, x2317
Math/CS Algebra Seminar

Abstract: The classifying space for elementary $p$-abelian extensions of a field $K$ has long been understood. If $K$ is a Galois extension of a field $F$, then the Galois group has a natural action on this classifying space, and --- at least when $\Gal(K/F)$ is a cyclic $p$-group --- one can develop a dictionary between a certain class of embedding problems and submodules of the corresponding Galois module. Combined with some surprising results concerning the module structure of the classifying space, this allows us to recover some interesting results on the structure of absolute Galois groups. If time permits, we will also discuss some generalizations of these modules and their potential for shedding further light on absolute Galois groups.

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