On the Voevodsky Motive of the Moduli Stack of Vector Bundles on a Curve
| Autor: | Victoria Hoskins, Simon Pepin Lehalleur |
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| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Intersection theory medicine.medical_specialty Conjecture Homotopy colimit Rank (linear algebra) General Mathematics 010102 general mathematics Vector bundle 01 natural sciences Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Mathematics::Category Theory Tensor (intrinsic definition) 0103 physical sciences FOS: Mathematics Torsion (algebra) medicine 010307 mathematical physics 0101 mathematics Algebraic Geometry (math.AG) Mathematics Stack (mathematics) |
| Zdroj: | The Quarterly Journal of Mathematics, 72, 1-2, pp. 71-114 The Quarterly Journal of Mathematics, 72, 71-114 |
| ISSN: | 1464-3847 0033-5606 |
| DOI: | 10.1093/qmathj/haaa023 |
| Popis: | 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. 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' |
| Databáze: | OpenAIRE |
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