Related papers: Dieudonne crystals and Wach modules for p-divisibl…

We derive new crystal melting models from Chern-Simons theory on the three-sphere. Via large N duality, these models compute amplitudes for A-model on the resolved conifold. The crystal is bounded by two walls whose distance corresponds to…

Let $G$ be a finite $p$-group with normal subgroup $N$, and $R$ a complete discrete valuation ring in mixed characteristic. We characterize permutation $RG$-modules in terms of modules for $RN$ and $R[G/N]$. The result generalizes both the…

The crystalline Chern classes of the value of a locally free crystal vanish on a smooth variety defined over a perfect field. Out of this we conclude new cases of de Jong's conjecture relating the geometric \'etale fundamental group of a…

We characterize those finite groups for which the bounded derived category of finite dimensional representations over an algebraically closed field of characteristic $p$ has distributive lattice of thick subcategories: they are precisely…

Let $p$ be an odd prime number, $K_{f}$ the finite unramified extension of $\mathbb{Q}_{p}$ of degree $f$, and $G_{K_{f}}$ its absolute Galois group. We construct analytic families of \'etale $(\varphi,\Gamma)$-modules which give rise to…

We study the crystal structure on categories of graded modules over algebras which categorify the negative half of the quantum Kac-Moody algebra associated to a symmetrizable Cartan data. We identify this crystal with Kashiwara's crystal…

We extend the results of Deligne and Illusie on liftings modulo $p^2$ and decompositions of the de Rham complex in several ways. We show that for a smooth scheme $X$ over a perfect field $k$ of characteristic $p>0$, the truncations of the…

We show that the multivariate additive higher Chow groups of a smooth affine $k$-scheme $\Spec (R)$ essentially of finite type over a perfect field $k$ of characteristic $\not = 2$ form a differential graded module over the big de Rham-Witt…

Let $K$ be an algebraically closed field of characteristic $p\geqslant 0$ and let $W$ be a finite-dimensional $K$-space of dimension greater than or equal to $5.$ In this paper, we give the structure of certain Weyl modules for…

Let $F$ be a finite extension of $\mathbb{Q}_p$. We determine the Lubin-Tate $(\varphi,\Gamma)$-modules associated to the absolutely irreducible mod $p$ representations of the absolute Galois group ${\rm Gal}(\bar{F}/F)$.

Let $K$ be a finite extension of $\mathbf{Q}_p$. We use the theory of $(\varphi,\Gamma)$-modules in the Lubin-Tate setting to construct some corestriction-compatible families of classes in the cohomology of $V$, for certain representations…

Let $K$ be a $p$-adic field and $T$ a lattice in a semistable representation of $\mathrm{Gal}(\overline{K}/K)$ with Hodge-Tate weights in $[0, r]$. Assuming $0\leq r<p-1$, we prove that for a semistable extension of $\mathbb{Z}_p$ by $T$,…

We apply crystal theory to affine Schubert calculus, Gromov-Witten invariants for the complete flag manifold, and the positroid stratification of the positive Grassmannian. We introduce operators on decompositions of elements in the…

We study relative Wach modules generalising our previous works on this subject. Our main result shows a categorical equivalence between relative Wach modules and lattices inside relative crystalline representations. Using this result, we…

Let F be a unramified finite extension of Qp and rhobar be an irreducible mod p two-dimensional representation of the absolute Galois group of F. The aim of this article is the explicit computation of the Kisin variety parameterizing the…

For a finite group scheme G over an algebraically closed field k of characteristic p>0 we study G-modules M, which are defined in terms of properties of their pull-backs along p-points of G. We show that the corresponding subcategories…

We construct stacks which algebraize Mazur's formal deformation rings of local Galois representations. More precisely, we construct Noetherian formal algebraic stacks over Spf Zp which parameterize \'etale (phi,Gamma)-modules; the formal…

For a variety $X$ separated over a perfect field of characteristic $p>0$ which admits an embedding into a smooth variety, we establish an anti-equivalence between the bounded derived categories of Cartier crystals on $X$ and constructible…

Let R be a complete rank-1 valuation ring of mixed characteristic (0,p), and let K be its field of fractions. A g-dimensional truncated Barsotti-Tate group G of level n over R is said to have a level-n canonical subgroup if there is a…

Every Anderson $A$-motive $M$ over a field determines a compatible system of Galois representations on its Tate modules at almost all primes of $A$. This adapts easily to $F$-isocrystals, which are rational analogues of $A$-motives for the…