• Corpus ID: 238634319

$\mathbb{A}^1$-connectivity of moduli of vector bundles on a curve

@inproceedings{Hogadi2021mathbbA1connectivityOM,
  title={\$\mathbb\{A\}^1\$-connectivity of moduli of vector bundles on a curve},
  author={Amit Hogadi and Suraj Yadav},
  year={2021}
}
  • A. Hogadi, Suraj Yadav
  • Published 12 October 2021
  • Mathematics
In this note we prove that the moduli stack of vector bundles on a curve, with a fixed determinant is A-connected. We obtain this result by classifying vector bundles on a curve upto A-concordance. Consequently we classify Pnbundles on a curve upto A-weak equivalence, extending a result in [2] of Asok-Morel. We also give an explicit example of a variety which is A-h-cobordant to a projective bundle over P but does not have the structure of a projective bundle over P, thus answering a question… 

References

SHOWING 1-7 OF 7 REFERENCES
Smooth varieties up to A^1-homotopy and algebraic h-cobordisms
We start to study the problem of classifying smooth proper varieties over a field k from the standpoint of A^1-homotopy theory. Motivated by the topological theory of surgery, we discuss the problem
A1-Algebraic Topology over a Field
1 Introduction.- 2 Unramified sheaves and strongly A1-invariant sheaves.- 3 Unramified Milnor-Witt K-theories.- 4 Geometric versus canonical transfers.- 5 The Rost-Schmid complex of a strongly
Comparing A^1-h-cobordism and A^1-weak equivalence
We study the problem of classifying projectivizations of rank-two vector bundles over ${\mathbb P}^2$ up to various notions of equivalence that arise naturally in ${\mathbb A}^1$-homotopy theory,
A homotopy theory for stacks
We give a homotopy theoretic characterization of stacks on a site C as the homotopy sheaves of groupoids on C. We use this characterization to construct a model category in which stacks are the
A1-homotopy theory of schemes
© Publications mathématiques de l’I.H.É.S., 1999, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://
Voevodsky: A 1 -homotopy theory of schemes
  • Inst. HautesÉtudes Sci. Publ. Math
  • 1999
Algebraic Geomtery
  • Graduate Texts in Mathematics No
  • 1977