Rational motivic path spacesand Kim’s relative unipotent section conjecture

Ishai Dan-Cohen; Tomer Schlank

doi:10.4171/RSMUP/97

Rational motivic path spacesand Kim’s relative unipotent section conjecture

Ishai Dan-Cohen, Tomer Schlank

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	117-172
Number of pages	56
Journal	Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova
Volume	148
DOIs	https://doi.org/10.4171/RSMUP/97
State	Published - 2022

Bibliographical note

Publisher Copyright:
© 2022 Università degli Studi di Padova Published by EMS Press.

Keywords

Rational homotopy
motivic homotopy
nonabelian Chabauty
rational points
unipotent fundamental group

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abstract = "We develop the foundations of commutative algebra objects in the category of motives, which we call “motivic dga{\textquoteright}s.” Works of White and Cisinski and D{\'e}glise 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{\textquoteright}s relative unipotent section conjecture into several smaller conjectures with a homotopical flavor.",

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Rational motivic path spacesand Kim’s relative unipotent section conjecture

Abstract

Bibliographical note

Keywords

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