Papers
Topics
Authors
Recent
Search
2000 character limit reached

A comparison theorem between Voevodsky's motives and motives with modulus in positive characteristic with rational coefficient

Published 23 Jan 2024 in math.AG | (2401.13119v2)

Abstract: In this note, without the assumption of resolution of singularities, we prove an equivalence between the category of motives with modulus in positive characteristic with rational coefficient $\MDM\eff(k,\Q)$ and Voevodsky's category of motives $\DM\eff(k,\Q)$, which has been philosophically predicted from the beginning in the study of motives with modulus.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (14)
  1. Refined alteration.
  2. Triangulated categories of logarithmic motives over a field, 2020.
  3. Semi-purity for cycles with modulus. arXiv:1812.01878, 2018.
  4. William Fulton. Intersection theory, volume 2 of Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics]. Springer-Verlag, Berlin, second edition, 1998.
  5. Points in algebraic geometry. J. Pure Appl. Algebra, 219(10):4667–4680, 2015.
  6. Motives with modulus, I: Modulus sheaves with transfers for non-proper modulus pairs. arXiv:1908.02975, 2019.
  7. Motives with modulus, II: Modulus sheaves with transfers for proper modulus pairs. arXiv:1910.14534, 2019.
  8. Motives with modulus, iii: The categories of motives. 2020.
  9. Modulus sheaves with transfers, 2021.
  10. Smooth blowup square for motives with modulus, 2019.
  11. Keiho Matsumoto. Gysin triangles in the category of motifs with modulus. Journal of the Institute of Mathematics of Jussieu, First View:1 – 24.
  12. Hiroyasu Miyazaki. Cube invariance of higher Chow groups with modulus. J. Algebraic Geom., 28(2):339–390, 2019.
  13. Bloch-Kato conjecture and motivic cohomology with finite coefficients. In The arithmetic and geometry of algebraic cycles (Banff, AB, 1998), volume 548 of NATO Sci. Ser. C Math. Phys. Sci., pages 117–189. Kluwer Acad. Publ., Dordrecht, 2000.
  14. Vladimir Voevodsky. Motivic cohomology groups are isomorphic to higher Chow groups in any characteristic. Int. Math. Res. Not., (7):351–355, 2002.

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We found no open problems mentioned in this paper.

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Authors (1)

  1. Keiho Matsumoto 

Collections

Sign up for free to add this paper to one or more collections.

Sign Up

Tweets

Sign up for free to view the 1 tweet with 10 likes about this paper.

Sign Up for Free