# Questions tagged [constructible-sheaves]

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### Constructible derived category and fundamental category

Introduction (may be skipped) Given a nice topological space $X$, the category of local systems (say over a field $k$) on it is equivalent to the category of representations of its fundamental ...
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### Epsilon factors - a la Beilinson - What is it?

I understand, to some extent, Tate's thesis. Could somebody explain perhaps what are the epsilon factors in Beilinson's works, such as "$\epsilon$-factors for Gauss-Manin determinants", or "...
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### Why do Kashiwara and Schapira require a base ring of finite global dimension?

In the book "Sheaves on Manifolds" by Kashiwara and Schapira, they work always with sheaves of $R$-modules, where $R$ is a ring of finite global dimension. Why do they do this, what care ...
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### Proof of Kashiwara's constructibility theorem for algebraic D-modules

I am trying to understand the proof of Kashiwara's constructibility theorem for algebraic D-modules, following either the book "D-modules, Perverse sheaves, and representation theory" by Hotta, ...
I'm looking for a proof of a theorem that is attributed to MacPherson. Treumann (Section 1.1 in Exit paths and constructible stacks, 2009) states the theorem as: Theorem 1.2 (MacPherson). Let $(X,S)... 0answers 208 views ### Category of representations of the path-groupoid The path-groupoid$\mathcal{P}_1(X)$of a (smooth) topological space$X$is a refinement of the fundamental groupoid$\Pi_1(X)$whose morphisms are given by (piecewise smooth) paths in$X$up to thin-... 0answers 374 views ### Purity and six operations? The six operations$f_!,f^!,f_*,f^*,\otimes,\mathcal Hom$have the property that they preserve estimates on weights in one direction. For$f_!,f^!,f_*,f^*$I can see, that they don't preserve purity ... 0answers 141 views ### Constructible sheaves on general stratified spaces I am not an expert in the field, so my question might be rather standard. Let$X$be a compact metric space. Assume that$X=\cup_{i=1}^NS_i$is a finite disjoint union of locally closed topological ... 0answers 477 views ### singular support of D-module smooth w.r.t. a stratification (1) Suppose that$X$is a smooth complex algebraic variety, stratified by some nice smooth stratification$S$. Let$M$be a$D$-module on$X$, s.t. its shriek-pullback (or star... whatever is ... 0answers 197 views ### Is there an analogue to the koszul complex for constructible sheaves? Given a variety$X$and a complete-intersection morphism $$Y \to X$$ is there an analogue of the Koszul complex for$\mathcal{O}_Y \in \textbf{Coh}(X)$in the setting of constructible sheaves? ... 0answers 192 views ### How to compute the first etale cohomology of a constructible torsion-free sheaf? I am interested in the following example! Let$k$be a field, let$X_0$be the scheme$\mathrm{Spec}R$with$R_0=k[x,y]/(xy)$, let$R$be the strict Hensilian localalisation of$R_0$at the origin ... 0answers 149 views ### Grothendieck group of constructible sets Let$K_0$be the Grothendieck group of complex algebraic varieties. This is the group generated by all complex algebraic varieties, subject to the relations: (i)$[X]=[Y]$if$X,Y$are isomorphic, (... 0answers 31 views ### If the set of non-0 stalks of F is relatively open, is the same true of its Verdier dual? Let$X$be a complex manifold,$F$a bounded complex of$\Bbb C_X$-modules with constructible cohomology. If the set$\{x: F_x\neq0\}$is relatively open (i.e. open in its closure), is the same true ... 0answers 98 views ### Continuity of constructible derived category Let$X_0$be a variety over$\mathbb F_q$. Denote by$X_n$its basechange to$\mathbb F_{q^n}$and let$X=\lim X_n$be its basechange to the algebraic closure$\overline{\mathbb F}_q$. Let$D^b_c(X_n,...
Let consider a quasicompact open $j:U\rightarrow\mathbb{A}^{\mathbb{N}}$ over a field $k$, Is there an example where $Rj_{*}\mathbb{Z}/n\mathbb{Z}$ is not constructible, where $n$ is prime to the ...