Questions tagged [constructible-sheaves]

The tag has no usage guidance.

15 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
359 views

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 ...
682 views

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 "...
302 views

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 ...
151 views

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 ...