モチーフ理論

投稿日：2025/10/19

一般

• Ayoub. Motives and algebraic cycles: a selection of conjectures and open queestions.

1-motive

• André. A Note on 1-Motives. HAL

Nori motive

• Ayoub, Barbieri-Viale. Nori 1-motives.
• Nori. TIFR での講義録
• Wangenheim. Nori-Motive und Tannaka-Theorie. arXiv:1111.5146
  • Huber–Müller-Stach を読めば良い？

Voevodsky motive

• Beilinson, Vologodsky. A DG guide to Voevodsky’s motives. arXiv:math/0604004.
• Levine. Motivic cohomology: past, present and future (slide).

motivic Galois group

• Ayoub の motivic Galois group：
  • Ayoub. L’algèbre de Hopf et le groupe de Galois motiviques d’un corps de caractéristique nulle I
  • ———. L’algèbre de Hopf et le groupe de Galois motiviques d’un corps de caractéristique nulle II
• Choudhury, Gallauer. An isomorphism of motivic Galois groups. arXiv:1410.6104
  • Nori の motivic Galois group と Ayoub の motivic Galois group の同型を示しているらしい．
• André. Groupes de Galois motivques et périodes. arXiv:1606.03714
  • Grothendieck, Nori, Voevodsky, Ayoub などによるモチーフの圏の構成のスケッチや，それらと周期の関係が紹介されている．

exponential motive

• Fresán, Jossen. Exponential motives
• Fresán. Euler’s constant and exponential motives (slide)
• ———. Exponential motives (CIRM での講演)

周期・超越性などとの関連

• Fresán. Une introduction aux périodes. arXiv:2210.03407
• Brown. Periods and Cosmic Galois group (slide)
• Klingler. Hodge theory, between algebraicity and transcendence. arXiv:2112.13814
  • モチーフではないが……
• Waldschmidt. Transcendence of Periods: The State of the Art
  • モチーフではないが……2

物理学との関連

• Cartier, Moussa, Julia, Vanhove. Frontiers in Number Theory, Physics, and Geometry II. Springer
  • Connes, Marcolli. Renormalization, the Riemann–Hilbert Correspondence, and Motivic Galois Theory. pp. 617–713. Springer.
• Connes, Marcolli. Noncommutative Geometry, Quantum Fields and Motives.
• Rej. Motives: an introductory survey for physicists.

そのほか

• Caramello. Motivic toposes. arXiv:1507.06271
• Barbieri-Viale. $\mathbb{T}$-motives. arXiv:1602.0505