Virtual rigid motives of semi-algebraic sets
| Autor: | Arthur Forey |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Ring (mathematics)
Pure mathematics 14C15 14F42 03C60 14G22 32S30 Root of unity General Mathematics 010102 general mathematics General Physics and Astronomy Field (mathematics) Algebraic variety Mathematics - Logic 01 natural sciences Commutative diagram Mathematics - Algebraic Geometry Morphism FOS: Mathematics 0101 mathematics Algebraic number Logic (math.LO) Motivic integration Algebraic Geometry (math.AG) Mathematics |
| Zdroj: | Selecta Mathematica. 25 |
| ISSN: | 1420-9020 1022-1824 |
| DOI: | 10.1007/s00029-019-0453-3 |
| Popis: | Let k be a field of characteristic zero containing all roots of unity and $$K=k(( t))$$ . We build a ring morphism from the Grothendieck ring of semi-algebraic sets over K to the Grothendieck ring of motives of rigid analytic varieties over K. It extends the morphism sending the class of an algebraic variety over K to its cohomological motive with compact support. We show that it fits inside a commutative diagram involving Hrushovski and Kazhdan’s motivic integration and Ayoub’s equivalence between motives of rigid analytic varieties over K and quasi-unipotent motives over k; we also show that it satisfies a form of duality. This allows us to answer a question by Ayoub, Ivorra and Sebag about the analytic Milnor fiber. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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