Rational motivic path spaces and Kim’s relative unipotent section conjecture
Rendiconti del Seminario Matematico della Università di Padova, Tome 148 (2022), pp. 117-172.
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We develop the foundations of commutative algebra objects in the category of motives, which we call “motivic dga’s.” Works of White and Cisinski and Déglise provide us with a suitable model structure. This enables us to reconstruct the unipotent fundamental group of a pointed scheme from the associated augmented motivic dga and provides us with a factorization of Kim’s relative unipotent section conjecture into several smaller conjectures with a homotopical flavor.

Publié le :
DOI : 10.4171/rsmup/97
Classification : 14, 55 
@article{RSMUP_2022__148__117_0,
     author = {Ishai Dan-Cohen and Tomer M. Schlank},
     title = {Rational motivic path spaces and {Kim{\textquoteright}s} relative unipotent section conjecture},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {117--172},
     volume = {148},
     year = {2022},
     doi = {10.4171/rsmup/97},
     mrnumber = {4542375},
     zbl = {07673824},
     language = {en},
     url = {http://www.numdam.org/articles/10.4171/rsmup/97/}
}
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Ishai Dan-Cohen; Tomer M. Schlank. Rational motivic path spaces and Kim’s relative unipotent section conjecture. Rendiconti del Seminario Matematico della Università di Padova, Tome 148 (2022), pp. 117-172. doi : 10.4171/rsmup/97. http://www.numdam.org/articles/10.4171/rsmup/97/

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