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Graduate Student Homotopy Theory Seminar: On the Lichtenbaum-Quillen conjectures in algebraic K theory

Event Type
243 Altgeld Hall
Oct 1, 2021   3:00 pm  
Likun Xie (PhD student, UIUC Mathematics)
Doron Grossman-Naples

Abstract: Starting with some motivations and brief expositions on algebraic K theory, I’ll introduce some early important computations of algebraic K theory, including computations of K theory of finite fields and of rings of integers for which I will briefly outline the proofs. Then we’ll move on to K theory with finite coefficients of separably closed fields.  With the motivation of recovering some information of K theory of an arbitrary field from its separable closure, we introduce a few versions of the Lichtenbaum-Quillen conjectures as descent spectrum sequences of etale Cohomology groups. If time permits, I’ll mention relation to motivic Cohomology that a key tool is some “motivic-to-K-theory” spectral sequence.

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