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

Massimo Pippi

• 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.