Motivic and \ell -adic realizations of the category of singularities of the zero locus of a global section of a vector bundle

Massimo Pippi ^[1]
1. [1] University College London
  
  University College London
  
  Reino Unido
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 2, 2022
Idioma: inglés
DOI: 10.1007/s00029-021-00734-2
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Resumen
- We study the motivic and ℓ-adic realizations of the dg category of singularities of the zero locus of a global section of a line bundle over a regular scheme. We will then use the formula obtained in this way together with a theorem due to D. Orlov and J. Burke–M. Walker to give a formula for the ℓ-adic realization of the dg category of singularities of the zero locus of a global section of a vector bundle. In particular, we obtain a formula for the ℓ-adic realization of the dg category of singularities of the special fiber of a scheme over a regular local ring of dimension n.