| Autor: |
Bass, Hyman, Oesterlé, Joseph, Weinstein, Alan, Bernstein, Joseph, Hinich, Vladimir, Melnikov, Anna, Kashiwara, M., Schapira, P., Ivorra, F., Waschkies, I. |
| Zdroj: |
Studies in Lie Theory; 2006, p171-221, 51p |
| Abstrakt: |
Let X be a C∞-manifold and T*X its cotangent bundle. We construct a microlocalization functor μX: Db(I($$ \mathbb{K}_X $$ )) → Db(I($$ \mathbb{K}_{T*X} $$ )), where Db(I($$ \mathbb{K}_X $$ )) denotes the bounded derived category of ind-sheaves of vector spaces on X over a field $$ \mathbb{K} $$ . This functor satisfies Rℌom(μX(F), μX(G)), ⋍ μhom(F,G) for any F,F ∈ Db($$ \mathbb{K}_X $$ ), thus generalizing the classical theory of microlocalization. Then we discuss the functoriality of μX. The main result is the existence of a microlocal convolution morphism $$ \mu _{X \times Y} \left( {\mathcal{K}_1 } \right)_ \circ ^a \mu _{Y \times Z} \left( {\mathcal{K}_2 } \right) \to \mu _{X \times Z} \left( {\mathcal{K}_1 \circ \mathcal{K}_2 } \right) $$ which is an isomorphism under suitable non-characteristic conditions on 171-10 and 171-11. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Supplemental Index |
| Externí odkaz: |
|
