Reidemeister Torsion for Vector Bundles on subscriptsuperscriptℙ1ℤ

We consider vector bundles of rank 2 with trivial generic fiber on the projective line over ℤ . For such bundles, a new invariant is constructed — the Reidemeister torsion, which is an analog of the classical Reidemeister torsion from topology. For vector bundles of rank 2 with trivial generic fiber...

Full description

Saved in:
Bibliographic Details
Published inProceedings of the Steklov Institute of Mathematics Vol. 325; no. Suppl 1; pp. S155 - S167
Main Author Polyakov, V. M.
Format Journal Article Conference Proceeding
LanguageEnglish
Published Moscow Pleiades Publishing 01.08.2024
Springer Nature B.V
Subjects
Invariants
Mathematics
Mathematics and Statistics
Topology
projective line
vector bundle
arithmetic surface
torsion
Online AccessGet full text
ISSN0081-5438
1531-8605
DOI10.1134/S008154382403012X

Cover

More Information
Summary:We consider vector bundles of rank 2 with trivial generic fiber on the projective line over ℤ . For such bundles, a new invariant is constructed — the Reidemeister torsion, which is an analog of the classical Reidemeister torsion from topology. For vector bundles of rank 2 with trivial generic fiber and jumps of height 1, that is, for the bundles that are isomorphic to superscript 𝒪 2 in the fiber over ℚ and are isomorphic to superscript 𝒪 2 or direct-sum 𝒪 1 𝒪 1 over each closed point of Spec ℤ , we calculate this invariant and show that it, together with the discriminant of the bundle, completely determines such a bundle.
Bibliography:ObjectType-Article-1
ObjectType-Feature-2
SourceType-Conference Papers & Proceedings-1
content type line 22
ISSN:0081-5438
1531-8605
DOI:10.1134/S008154382403012X