Hodge Theory and $L^2$-analysis

## Deligne-Beilinson Cohomology of Affine Groups

Publication
, Chapter

Hain, R

2017

The goal of this paper is to develop the theory of Deligne-Beilinson cohomology of affine groups with a mixed Hodge structure. The motivation comes from Hodge theory and the study of motives, where such groups appear. Several of Francis Brown's period computations (arXiv:1407.5167) are interpreted as elements of the DB cohomology of the relative unipotent completion of $SL_2(Z)$ and their cup products. The results in this paper are used in arXiv:1403.6443 where they are used to prove that Pollack's quadratic relations are motivic.

### Duke Scholars

## ISBN

9781571463517

## Publication Date

2017

## Publisher

International Press

## Related Subject Headings

- General Mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics

### Citation

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Chicago

ICMJE

MLA

NLM

Hain, R. (2017). Deligne-Beilinson Cohomology of Affine Groups. In L. Ji (Ed.),

*Hodge Theory and $L^2$-analysis*. International Press.Hain, R. “Deligne-Beilinson Cohomology of Affine Groups.” In

*Hodge Theory and $L^2$-Analysis*, edited by L. Ji. International Press, 2017.Hain R. Deligne-Beilinson Cohomology of Affine Groups. In: Ji L, editor. Hodge Theory and $L^2$-analysis. International Press; 2017.

Hain, R. “Deligne-Beilinson Cohomology of Affine Groups.”

*Hodge Theory and $L^2$-Analysis*, edited by L. Ji, International Press, 2017.Hain R. Deligne-Beilinson Cohomology of Affine Groups. In: Ji L, editor. Hodge Theory and $L^2$-analysis. International Press; 2017.

## ISBN

9781571463517

## Publication Date

2017

## Publisher

International Press

## Related Subject Headings

- General Mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics