Cohomologie des foncteurs polynomiaux sur les groupes libres
- Submitting institution
-
The University of Leicester
- Unit of assessment
- 10 - Mathematical Sciences
- Output identifier
- 1298
- Type
- D - Journal article
- DOI
-
-
- Title of journal
- Documenta Mathematica
- Article number
- -
- First page
- 205
- Volume
- 21
- Issue
- 2016
- ISSN
- 1431-0643
- Open access status
- Out of scope for open access requirements
- Month of publication
- -
- Year of publication
- 2016
- URL
-
-
- Supplementary information
-
-
- Request cross-referral to
- -
- Output has been delayed by COVID-19
- No
- COVID-19 affected output statement
- -
- Forensic science
- No
- Criminology
- No
- Interdisciplinary
- No
- Number of additional authors
-
2
- Research group(s)
-
A - Algebra and Geometry
- Proposed double-weighted
- No
- Reserve for an output with double weighting
- No
- Additional information
- -
- Author contribution statement
- -
- Non-English
- Yes
- English abstract
- We show that extension groups between two polynomial functors on free groups are the same in the category of all functors and in subcategory Fd of polynomial functors of degree ≤ d. Moreover, we show that the derived category D(Z[Sd]) of the group ring of the symmetric groups is fully embedded in the derived category of Fd. The proof relies on functorial properties of the group ring of free groups and its filtration by powers of the augmentation ideal. We give some applications; particularly that in certain cases the global dimension of the category of Fd is d - 1.