Related papers: Product formula for p-adic epsilon factors

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 show that the arithmetic D-module associated to an overconvergent F-isocrystal over a smooth curve is holonomic. We first prove that unipotent F-isocrystals are holonomic D-module by using the fact that such F-isocrystals come from…

We prove the overholonomicity of overconvergent $F$-isocrystals over smooth varieties. This implies that the notions of overholonomicity and devissability in overconvergent $F$-isocrystals are equivalent. Then the overholonomicity is stable…

We study the $p$-adic (generalized) hypergeometric equations by using the theory of multiplicative convolution of arithmetic $\mathscr{D}$-modules. As a result, we prove that the hypergeometric isocrystals with suitable rational parameters…

Let $k$ be a perfect field of characteristic $p >0$, $U$ be a variety over $k$ and $F$ be a power of Frobenius. We construct the category of overholonomic arithmetical ($F$-)$\D$-modules over $U$ and the category of overholonomic…

We prove that in either the convergent or overconvergent setting, an absolutely irreducible $F$-isocrystal on the absolute product of two or more smooth schemes over perfect fields of characteristic $p$, further equipped with actions of the…

Let $p$ be a fixed prime number and let $R$ denote a uniserial $p$-adic space group of dimension $d_x=(p-1)p^{x-1}$ and with cyclic point group of order $p^x$. In this short note we prove that all the quotients of $R$ of size bigger than or…

Let $\mathcal{V}$ be a mixed characteristic complete discrete valuation ring, $k$ its residual field, $\mathcal{P}$ a proper smooth formal scheme over $\mathcal{V}$, $P$ its special fiber, $T$ a divisor of $P$, $U:=P\setminus T$, $Y$ a…

Let $X$ be a smooth scheme over a finite field of characteristic $p$. In answer to a conjecture of Deligne, we establish that for any prime $\ell \neq p$, an $\ell$-adic Weil sheaf on $X$ which is algebraic (or irreducible with finite…

We use the stacky approach to $p$-adic cohomology theories recently developed by Drinfeld and Bhatt--Lurie to generalise a comparison theorem between the rational crystalline cohomology of the special fibre and the rational $p$-adic \'etale…

This note provides truncated formulae with explicit error terms to compute Euler products over primes in arithmetic progressions of rational fractions. It further provides such a formula for the product of terms of the shape $F(1/p, 1/p^s)$…

In this paper, we prove that for any $p$-adic smooth separated formal scheme $\mathfrak X$, the category of prismatic $F$-crystals with $I$ inverted is equivalent to the category of \'etale $\mathbb Z_p$-local systems on the generic fiber…

For varieties over a perfect field of characteristic p, etale cohomology with Q_l-coefficients is a Weil cohomology theory only when l is not equal to p; the corresponding role for l = p is played by Berthelot's rigid cohomology. In that…

We introduce a new category of coefficients for p-adic cohomology called constructible isocrystals. Conjecturally, the category of constructible isocrystals endowed with a Frobenius structure is equivalent to the category of perverse…

In this paper we prove some generalizations of the classical Hasse-Davenport product relation for certain arithmetic factors defined on p-adic fields, among them one finds the epsilon-factors appearing in Tate's thesis. We then show that…

Let $X$ be a smooth variety over a finite field $\mathbb{F}_q$. Let $\ell$ be a rational prime number invertible in $\mathbb{F}_q$. For an $\ell$-adic sheaf $\mathcal{F}$ on $X$, we construct a cycle supported on the singular support of…

The purpose of this paper is to prove a basic $p$-adic comparison theorem for smooth rigid analytic and dagger varieties over the algebraic closure $C$ of a $p$-adic field: $p$-adic pro-\'etale cohomology, in a stable range, can be…

Let $X$ be a smooth projective curve over a finite field of characteristic $p$. We describe and implement a practical algorithm for computing the $p$-divisible group $Jac(X)[p^\infty]$ via computing its Dieudonn\'{e} module, or equivalently…

We show that, under fairly general conditions, many elements of a p-adic group can be well approximated by a product whose factors have properties that are helpful in performing explicit character computations.

Ardakov-Wadsley defined the sheaf D-cap of $p$-adic analytic differential operators on a smooth rigid analytic variety $X$ by restricting to the case where $X$ is affinoid and the tangent sheaf admits a smooth Lie lattice. We generalize…