Report
On the Voevodsky motive of the moduli stack of vector bundles on a curve
| العنوان: | On the Voevodsky motive of the moduli stack of vector bundles on a curve |
|---|---|
| المؤلفون: | Hoskins, Victoria, Lehalleur, Simon Pepin |
| سنة النشر: | 2017 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry |
| الوصف: | We define and study the motive of the moduli stack of vector bundles of fixed rank and degree over a smooth projective curve in Voevodsky's category of motives. We prove that this motive can be written as a homotopy colimit of motives of smooth projective Quot schemes of torsion quotients of sums of line bundles on the curve. When working with rational coefficients, we prove that the motive of the stack of bundles lies in the localising tensor subcategory generated by the motive of the curve, using Bialynicki-Birula decompositions of these Quot schemes. We conjecture a formula for the motive of this stack, and we prove this conjecture modulo a conjecture on the intersection theory of the Quot schemes. Comment: 32 pages. We have moved the section on Bialynicki-Birula decompositions (Section 3 in v1) to another joint paper entitled 'On the Voevodsky motive of the moduli space of Higgs bundles on a curve' |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1711.11072 |
| رقم الانضمام: | edsarx.1711.11072 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |