Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Algebraic Geometry

arXiv:2201.06162 (math)
[Submitted on 17 Jan 2022 (v1), last revised 11 Mar 2024 (this version, v7)]

Title:Chow motives of genus one fibrations

Authors:Daiki Kawabe
View PDF HTML (experimental)
Abstract:Let $f: X \rightarrow C$ be a genus 1 fibration from a smooth projective surface, i.e. its generic fiber is a regular genus 1 curve. Let $j: J \rightarrow C$ be the Jacobian fibration of $f$. In this paper, we prove that the Chow motives of $X$ and $J$ are isomorphic. As an application, combined with our concomitant work on motives of quasi-elliptic fibrations, we prove Kimura finite-dimensionality for smooth projective surfaces not of general type with geometric genus 0. This generalizes Bloch-Kas-Lieberman's result to arbitrary characteristic.
Comments: 36 pages. Minor revisions. The abstract has been revised according to the referee's helpful comments. To appear in Manuscripta Mathematica
Subjects: Algebraic Geometry (math.AG)
MSC classes: 14C15, 14J27, 14J28
Cite as: arXiv:2201.06162 [math.AG]
  (or arXiv:2201.06162v7 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.2201.06162

Submission history

From: Daiki Kawabe [view email]
[v1] Mon, 17 Jan 2022 00:14:05 UTC (283 KB)
[v2] Thu, 27 Jan 2022 04:20:33 UTC (283 KB)
[v3] Mon, 7 Feb 2022 23:27:38 UTC (484 KB)
[v4] Tue, 30 May 2023 00:27:32 UTC (36 KB)
[v5] Tue, 14 Nov 2023 01:07:24 UTC (34 KB)
[v6] Tue, 30 Jan 2024 01:46:29 UTC (36 KB)
[v7] Mon, 11 Mar 2024 23:34:06 UTC (36 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.AG
< prev   |   next >
new | recent | 2022-01
Change to browse by:
math

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)