The equivariant motivic cohomology of varieties of long exact sequences
Abstract/Contents
- Abstract
- A perfect field, $k$, is fixed throughout. The aim of the present work is to compute the equivariant motivic cohomology of a certain variety, $X$, which represents the space of long exact sequences of given length and with prescribed ranks, all in the category of finite dimensional $k$-vector spaces, equivariant with respect to an action of the multiplicative group scheme of $k$. In order to calculate this, it is necessary to establish a number of results pertaining to the motivic cohomology of the general linear group scheme, and to introduce a spectral sequence for deriving the motivic cohomology of homogeneous varieties. We then present the variety $X$ as a homogeneous variety, and so obtain the cohomology. As an application, we show that the cohomology furnishes obstructions to equivariant maps from punctured affine $n$-spaces to $X$, which amounts to the same thing as obstructions to the existence of certain differential graded modules over polynomial rings over $k$. The obstructions so found are a generalization of the Herzog-K\"uhl equations, which are well-known in the particular case where the differential graded module is in fact a resolution of an Artinian module.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2010 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Williams, Thomas Benedict |
|---|---|
| Associated with | Stanford University, Department of Mathematics |
| Primary advisor | Carlsson, G. (Gunnar), 1952- |
| Thesis advisor | Carlsson, G. (Gunnar), 1952- |
| Thesis advisor | Cohen, Ralph L, 1952- |
| Thesis advisor | Vakil, Ravi |
| Advisor | Cohen, Ralph L, 1952- |
| Advisor | Vakil, Ravi |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Thomas Benedict Williams. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2010. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2010 by Thomas Benedict Williams
- License
- This work is licensed under a Creative Commons Attribution Share Alike 3.0 Unported license (CC BY-SA).
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