# Noninvertible cohomology and the Teichmüller cocycle

Seminar
Speaker
Prof. Darrell Haile (Indiana University)
Date
19/03/2014 - 10:30Add to Calendar 2014-03-19 10:30:00 2014-03-19 10:30:00 Noninvertible cohomology and the Teichmüller cocycle Noninvertible cohomology refers to Galois cohomology in which the values of the cocycles are allowed to be noninvertible.  In this talk I will describe an application of this theory to the following problem: Given L/F, a finite separable extension of fields, and an L-central simple algebra B, classify those F-algebras A containing B that are "tightly connected to B" in a sense I will make precise.  The answer uses the Teichmüller cocycle.  This is a three-cocycle that is the obstruction, when L/F is Galois, to a normal L/F central simple algebra (i.e. a central simple L-algebra B with the property that every element of Gal(L/F) extends to an automorphism of B) having the property that its Brauer class in Br(L) is restricted from B(F).  This is mostly work of two of my students, Holly Attenborough and Kevin Foster. אוניברסיטת בר-אילן - המחלקה למתמטיקה mathoffice@math.biu.ac.il Asia/Jerusalem public
Abstract

Noninvertible cohomology refers to Galois cohomology in which the values of the cocycles are allowed to be noninvertible.  In this talk I will describe an application of this theory to the following problem: Given L/F, a finite separable extension of fields, and an L-central simple algebra B, classify those F-algebras A containing B that are "tightly connected to B" in a sense I will make precise.  The answer uses the Teichmüller cocycle.  This is a three-cocycle that is the obstruction, when L/F is Galois, to a normal L/F central simple algebra (i.e. a central simple L-algebra B with the property that every element of Gal(L/F) extends to an automorphism of B) having the property that its Brauer class in Br(L) is restricted from B(F).  This is mostly work of two of my students, Holly Attenborough and Kevin Foster.

תאריך עדכון אחרון : 20/03/2014