MATH Seminar
| Title: On Serre-Grothendieck and Purity conjectures for groups of type $F_4$ |
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| Seminar: Algebra |
| Speaker: Vladimir Chernousov of University of Alberta |
| Contact: R. Parimala, parimala@mathcs.emory.edu |
| Date: 2010-03-16 at 4:00PM |
| Venue: MSC W303 |
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| Abstract: The Grothendieck-Serre conjecture asserts that for a reductive group $G$ over a smooth affine scheme $X$ a rationally trivial $G$-torsor is trivial in Zariski topology or more generally if $R$ is a regular local ring and $G$ is a reductive group scheme over $R$ then the natural mapping $f:H^1(R,G)\to H^1(K,G)$ has trivial kernel. Here $K$ is a fraction field of $R$. The image of $f$ is described by the purity conjecture which says that a $G$-torsor over $K$ is in the image of $f$ if and ony if it is unramified everywhere in codimension $1$. These two conjectures are known for many groups of classical types and type $G_2$. In my talk we discuss next open case of groups of type $F_4$. |
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