Zobrazeno 1 - 10
of 58
pro vyhledávání: '"Dupont, Clement"'
We develop the theory of ``virtual morphisms'' in logarithmic algebraic geometry, introduced by Howell. It allows one to give algebro-geometric meaning to various useful maps of topological spaces that do not correspond to morphisms of (log) schemes
Externí odkaz:
http://arxiv.org/abs/2408.13108
Autor:
Dupont, Clément
Mixed Tate motives are central objects in the study of cohomology groups of algebraic varieties and their arithmetic invariants. They also play a crucial role in a wide variety of questions related to multiple zeta values and polylogarithms, algebrai
Externí odkaz:
http://arxiv.org/abs/2404.03770
Autor:
Dupont, Clément
Publikováno v:
La Gazette de La Soci\'et\'e Math\'ematique de France 178 (octobre 2023)
This text was published in the Gazette de la Soci\'et\'e Math\'ematique de France in October 2023. It is an introduction to the theory of motives, from its sources to its more modern developments.
Comment: In French. 20 pages, 4 figures (all by
Comment: In French. 20 pages, 4 figures (all by
Externí odkaz:
http://arxiv.org/abs/2401.11227
We introduce a natural geometric framework for the study of logarithmically divergent integrals on manifolds with corners and algebraic varieties, using the techniques of logarithmic geometry. Key to the construction is a new notion of morphism in lo
Externí odkaz:
http://arxiv.org/abs/2312.17720
Autor:
Dupont, Clément, Fresán, Javier
Classical polylogarithms give rise to a variation of mixed Hodge-Tate structures on the punctured projective line $S=\mathbb{P}^1\setminus \{0, 1, \infty\}$, which is an extension of the symmetric power of the Kummer variation by a trivial variation.
Externí odkaz:
http://arxiv.org/abs/2305.00789
Autor:
Dupont, Clément
Publikováno v:
S\'eminaire Bourbaki, 72\`eme ann\'ee, 2019-2021, no. 1176, 294-343
This survey article is the written version of a talk given at the Bourbaki seminar in April 2021. We give an introduction to Zagier's conjecture on special values of Dedekind zeta functions, and its relation to $K$-theory of fields and the theory of
Externí odkaz:
http://arxiv.org/abs/2109.01702
Autor:
Dupont, Clément
This survey article is the written version of two talks given at the Journ\'ees X-UPS 2019 "P\'eriodes et transcendance" at \'Ecole polytechnique. We give a gentle introduction to the study of multiple zeta values, from Euler's solution to the Basel
Externí odkaz:
http://arxiv.org/abs/2109.01699
Autor:
Dupont, Clément, Juteau, Daniel
Publikováno v:
Algebr. Geom. Topol. 24 (2024) 1431-1466
We construct and study a motivic lift of a spectral sequence associated to a stratified scheme, recently discovered by Petersen in the context of mixed Hodge theory and $\ell$-adic Galois representations. The original spectral sequence expresses the
Externí odkaz:
http://arxiv.org/abs/2003.04217
Autor:
Brown, Francis, Dupont, Clément
Publikováno v:
Comm. Math. Phys. 382 (2021), 815-874
We study open and closed string amplitudes at tree-level in string perturbation theory using the methods of single-valued integration which were developed in the prequel to this paper. Using dihedral coordinates on the moduli spaces of curves of genu
Externí odkaz:
http://arxiv.org/abs/1910.01107
Autor:
Brown, Francis, Dupont, Clément
Publikováno v:
Nagoya Math. J. 249 (2023), 148-220
The goal of this paper is to raise the possibility that there exists a meaningful theory of `motives' associated to certain hypergeometric integrals, viewed as functions of their parameters. It goes beyond the classical theory of motives, but should
Externí odkaz:
http://arxiv.org/abs/1907.06603