Overholonomic arithmetical D-modules

Overcoherence implies holonomicity

Let $\V$ be a mixed characteristic complete discrete valuation ring with perfect residue field. Let $\X$ be a smooth formal scheme over $\V$. We prove than a $\D ^†_{\X,\Q} $-module which is overcoherent after any change of basis is an holonomic $\D ^†_{\X,\Q} $-module. Furthermore, we check that this implies than a bounded complex $\E$ of $\D ^†_{\X,\,\Q}$-modules is overholonomic after any change of basis if and only if, for any integer $j$, $\mathcal{H} ^{j} (\E) $ is overholonomic after any change of basis.

Logarithmic $p$-bases and arithmetical differential modules

We introduce the notion of log $p$-smoothness which weakens that of log-smoothness and that of having locally $p$-bases. We extend Berthelot's construction of arithmetic $D$-modules and some properties in this context.

p进GKZ超几何D-模与复形的比较定理

A Comparison Theorem for $p$-adic GKZ Hypergeometric $\mathcal D$-Modules and Complexes

本文比较p进GKZ超几何复形与超几何算术D-模，在特定条件下证明比较态射为拟同构，还建立复形的次数集中性、全纯性，构造Frobenius结构并证明其限制为特定过收敛F-等晶体。

全微分D-cap模在刚性解析空间上的全纯性

Holonomic D-cap-modules on rigid analytic spaces

本文定义了刚性解析空间上的全微分D-cap模，并证明了其在五种操作下的稳定性，同时探讨了其与常规六 functor 形式的关系。

On the stability by tensor products of complexes of arithmetic D-modules

Let $V$ be a complete discrete valued ring of mixed characteristic $(0,p)$, $K$ its field of fractions, $k$ its residue field which is supposed to be perfect. Let $X$ be a separated $k$-scheme of finite type and $Y$ be a smooth open of $X$. We check that the equivalence of categories $sp_{(Y,X),+}$ (from the category of overconvergent isocrystals on $(Y,X)/K$ to that of overcoherent isocrystals on $(Y,X)/K$) commutes with tensor products. Next, in Berthelot's theory of arithmetic $\mathcal{D}$-modules, we prove the stability under tensor products of the devissability in overconvergent isocryst…

算术$\mathscr{D}$-模的刚性化与过收敛黎曼-希尔伯特对应

Rigidification of arithmetic $\mathscr{D}$-modules and an overconvergent Riemann-Hilbert correspondence

本文在正特征域上构造可构造等晶体的三角范畴，建立其与过完整$\mathscr{D}^\dagger$-模的黎曼-希尔伯特等价，并证明刚性上同调与算术$\mathscr{D}$-模上同调一致。