The constructible-sheaves tag has no usage guidance.

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### 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 ...

**2**

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**1**answer

194 views

### Higher direct image of locally constant torsion sheaf (étale cohomology)

Let $\phi:X\rightarrow Y$ be a generically smooth projective surjective morphism of algebraic varieties over $k=\bar k.$ Is it possible for $R^1\phi_*(\mathbb Z/l)$ to be supported on a divisor of $Y$ ...

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242 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 ...

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51 views

### constructibility for pushforward

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 ...

**2**

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**1**answer

221 views

### Nearby cycles and specialisation - properties

I am looking for reference for properties of nearby cycles - specifically, commutation with non-characteristic pull-back (good enough - commutation with pull-back to closed subvariety which is ...

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375 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 "...

**2**

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82 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,...

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**2**answers

205 views

### on a characterisation of the intersection complex

Let $X$ be an integral scheme of finite type over a field $k$ of dimension $d$ and $U$ an open dense smooth subscheme.
Let $K\in D_{c}^{b}(X,\bar{\mathbb{Q}}_{l})$ be such that $K_{U}=\bar{\mathbb{Q}}...

**4**

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302 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 ...

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258 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 ...

**14**

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260 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 ...

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**1**answer

233 views

### Vanishing of !-restriction of constructible sheaves

If $\mathcal F$ is a constructible sheaf (say of $\mathbb C$-modules) on a (real) manifold concentrated in degree $0$ and $i\colon Z \hookrightarrow X$ is a submanifold, can I say anything about $H^j(...

**4**

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**1**answer

503 views

### Analogues of D-modules and constructible sheaves

For a smooth complex variety, one can consider the category of say holonomic $\mathcal D$ modules on it. It is equipped with the deRham functor, which turns a $\cal D$-module into a constructible ...

**2**

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278 views

### Reference wanted - preservation of constructible sheaves (in classical topology) by all functors

Hello,
Can anybody point to me a reference about the preservation of the derived bounded category of sheaves with constructible cohomology on the underlying classical (anayltic) space of a complex ...

**6**

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**1**answer

715 views

### Constructible sheaves and dg-modules

Let $M$ be a smooth manifold, $A_M$ the de Rham algebra of $M$, $D_{A_M}$ the derived category of the category of differential graded (dg) $A_M$-modules and $D^+_c(M)$ the bounded below constructible ...