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**19**

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628 views

### What is classified by the (big) crystalline topos?

In his paper "Generic Galois Theory of Local Rings", G.C. Wraith states on p. 743 that the (big) crystalline topos "can be conveniently described in terms of the theory it describes". What exactly is ...

**11**

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328 views

### Is there a notion of tensor product of perfect bases of representations of Lie algebras?

Berenstein and Kazhdan define perfect bases as an "unquantized" version of crystal bases. A perfect basis is roughly a basis with a crystal structure such that $E_i\cdot v=\mathbb{C}\cdot \tilde{e}...

**9**

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197 views

### Good bounds for the number of $n$-dimensional crystallographic groups ?

Let $s(n)$ denote the number of distinct crystallographic groups in $Isom(\mathbb{R}^n)$.
Apparently the best known upper bound so far is
$$
s(n)\le e^{e^{4n^2}},
$$
given by Peter Buser in $1985$. On ...

**5**

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108 views

### (Double) Crystal reflection operators on SSYTs

I am not that familiar with the language of crystals, but this is what I know:
Let $SSYT(\lambda, \mu)$ be the set of semi-standard Young tableaux with shape $\lambda$ and weight $\mu$.
There are ...

**3**

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146 views

### Relation between crystalline and perverse sheaves

Take $X$ to be a smooth complex projective algebraic variety. The Riemann-Hilbert correspondence gives an equivalence of categories between the category of perverse sheaves on $X$ and the category of ...

**2**

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368 views

### $\sigma$-conjugate iff $p$-adically close

First some notations. Let $p$ be a prime, $k$ a perfect field of characteristic $p$, $W=W(k)$ the ring of Witt vectors over $k$, $\sigma : W \rightarrow W$ the Frobenius, $R$ a commutative $\mathbb{Z}...

**1**

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148 views

### Two different definitions of $\sigma$-L-spaces in Kottwitz I and II

In his papers "Isocrystals with additional structure" I and II, Kottwitz defines the notion of $\sigma$-$L$-spaces. In the first one the situation is the following
$k$ an algebraically closed field ...