相关论文: The Pro-\'Etale Topos as a Category of Pyknotic Pr…

For $p \geqslant 3$ and an unramified extension $F/\mathbb{Q}_p$ with perfect residue field, we define a syntomic complex with coefficients in a Wach module over a certain period ring for $F$. We show that our complex computes the…

We study the \'{e}tale fundamental groups of singular reduced connected curves defined over an algebraically closed field of arbitrary prime characteristic. It is shown that when the curve is projective, the \'{e}tale fundamental group is a…

In Proposition I of "Memoire sur les conditions de resolubilite des equations par radicaux", Galois established that any intermediate extension of the splitting field of a polynomial with rational coefficients is the fixed field of its…

We construct a $\bar Q_l$-linear Tannakian category attached to a smooth projective curve C equivalent to the category of finite dimensional $\bar Q_l$-representations Rep(G), where G is $Sp(2g-2,\bar Q_l)$ or $Sl(2g-2,\bar Q_l)$ depending…

We introduce the notions of a half-balanced braided monoidal category and of its contraction. These notions give rise to an explicit description of the action of the Galois group of QQ on Teichmueller groupoids in genus 0, equivalent to…

We provide a general construction of induced $t$-structures, that generalizes standard $t$-structures for $\infty$-categories of sheaves. More precisely, given a presentable $\infty$-category $\mathcal{X}$ and a presentable stable…

Based on the analogies between mapping class groups and absolute Galois groups, we introduce an arithmetic pro-$\ell$ analogue of Orr invariants for a Galois element associated with Galois action on \'etale fundamental groups of punctured…

We give necessary conditions for a category fibred in pseudo-abelian additive categories over the classifying topos of a profinite group to be a stack; these conditions are sufficient when the coefficients are $\mathbf{Q}$-linear. This…

By two well-known results, one of Ax, one of Lubotzky and van den Dries, a profinite group is projective iff it is isomorphic to the absolute Galois group of a pseudo-algebraically closed field. This paper gives an analogous…

We define a pro-$p$ Abelian sheaf on a modular curve of a fixed level $N \geq 5$ divisible by a prime number $p \neq 2$. Every $p$-adic representation of $\text{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$ associated to an eigenform is obtained…

Associated to a presentable $\infty$-category $\mathcal{C}$ and an object $X \in \mathcal{C}$ is the tangent $\infty$-category $\mathcal{T}_X\mathcal{C}$, consisting of parameterized spectrum objects over $X$. This gives rise to a…

We construct the crystalline comparison isomorphisms for proper smooth formal schemes over an absolutely unramified base. Such isomorphisms hold for \'etale cohomology with nontrivial coefficients, as well as in the relative setting, i.e.…

Let $k$ be an algebraically closed field of exponential characteristic $p$. Given any prime $\ell\neq p$, we construct a stable \'etale realization functor $$\underline{\text{\'Et}}_{\ell}:\text{Spt}(k)\rightarrow…

Let $K/E/\mathbb{Q}_p$ be a tower of finite extensions with $E$ Galois. We relate the category of $G_K$-equivariant vector bundles on the Fargues--Fontaine curve with coefficients in $E$ with $E$-$G_K$-$B$-pairs and describe crystalline and…

If $G$ is a finite group or a torus, it is known that there is an isomorphism between the Grothendieck group of homotopy representations and that of generalized homotopy representations for $G$. We prove that there is such an isomorphism…

\emph{Proto-exact categories}, introduced by Dyckerhoff and Kapranov, are a generalization of Quillen exact categories which provide a framework for defining algebraic K-theory and Hall algebras in a \emph{non-additive} setting. This…

To any triangulated category with tensor product $(K,\otimes)$, we associate a topological space $Spc(K,\otimes)$, by means of thick subcategories of $K$, a la Hopkins-Neeman-Thomason. Moreover, to each open subset $U$ of $Spc(K,\otimes)$,…

We propose a construction of a stable category for any pretorsion theory in a lextensive category. We prove the universal property of the stable category, that extends previous results obtained for the stable category of internal preorders…

We exhibit a geometric morphism from the Grothendieck topos representing the Solovay model to the $\kappa$-pyknotic sets of Barwick--Haine and Clausen--Scholze. We then use the properties of this morphism and automatic continuity in the…

Let $X$ be a smooth symplectic variety over a field $k$ of characteristic $p>2$ equipped with a restricted structure, which is a class $[\eta] \in H^0(X, \Omega^1_X/d\mathcal O_X)$ whose de Rham differential equals the symplectic form. In…