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--- blog:2023-04-22 [2023/04/22 10:25] – created pzhou
+++ blog:2023-04-22 [2023/06/25 15:53] (current) – external edit 127.0.0.1
@@ Line 13: / Line 13: @@
 Now, here are the problems
-==== 1 ====
+==== Major Issues ====
-Where is the key estimate
+=== 1 ===
+Where is the key estimate
+$$ SS(\pi_* Sh(\La_B)) \In \pi_*(SS(Sh(\La_B)) $$
+established?
+A similar estimate for sheaves valued in stable category is well-known (hmm, my stuff is also stable, right? closed under cones etc). So, is my notion of singular support different from the standard one?
+Hmm, I justed bluffed that this is obvious, but now I am caught here. But, why is it not obvious? Naively, the singular support of a sheaf of anything is defined by the nearby cycle functor, no?
+OK, I see. The referee is complaining I am using a seemingly different notion of singular support for categories than Kashiwara-Schapira. Indeed, when the space is stratified, and we have a priori bound, then maybe we can use the old notion.
+OK, indeed, I will say singular support for stable categories as is, and only remark that in case of constructible sheaves, this can be checked without much effort.
+Not a big deal :)
+=== 2 ===
+Aha, classically generate means the smallest stable subcategories that contains these object.
+Good question, why do they generate, well because back in $\La_{\C^N}$, they compactly generate the large category.
+As David Nadler says "the only nice construction in category is universal construction'.
+ok,this is already on p22.
+=== 3 ===
+Not a big deal, just need to add: because in this grid stratified case, singular support can be estimated easily.
+==== Minor Issues ====
+. I really need to be precise! ahh. being complained. so, let me be more precise. Constructible sheaf with stratification $S$ is related to Lagrangians with singular support $\Lambda_S$.
+. yes, Segal introduced this notion.
+. better reference habit, give precise reference. Yes, we understand you are lazy, but please don't be lazy.
+. give reference to the later introduced FLTZ skeleton.
+. indeed, the notion of partially wrapped CCC is new. let me think how to recover that. I think this is best done by this: starting from the equivariant CCC, then on the B-side, we de-equivariantize on a subgroup, meaning we forget the equivariant structure.
+...
+. yes, forward reference about symplectic reduction should be given.
+.