Quantitative Tamarkin Theory by Jun Zhang

Author:Jun Zhang
Language: eng
Format: epub
ISBN: 9783030378882
Publisher: Springer International Publishing

Instead of computing RHom(ℱ, G) directly, we will rewrite it in terms of a new sheaf (people usually call it internal hom in T(M)), denoted by ℋom ∗(ℱ, G). Here is a precise statement.

Lemma 3.3

For any ℱ, G ∈ T(M),

(3.10)

where is the projection. The sheaf of ℋom ∗(ℱ, G) is introduced in Definition 3.10.

Note that Rπ ∗ℋom ∗(ℱ, G) on the right-hand side of the identity (3.10) is in general a complex of sheaves over , which reduces considerably the difficulty of the discussion and computations. Moreover, under a constructibility assumption, where the type of intervals is determined by the singular support of ℋom ∗. Then we are able to compute the right-hand side of (3.10) based on Theorem 3.2 or Example 3.13. This will be particularly helpful in Sect. 3.9. Last but not least, we want to emphasize that what the Separation Theorem really establishes is that sheaf Rπ ∗ℋom ∗(ℱ, G) = 0.

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