Related papers: Picard groups in $p$-adic Fourier theory

Let $G$ be a finite group. For a $G$-ring $A,$ let ${\rm Pic}^{\it G}({\it A})$ denote the equivariant Picard group of $A.$ We show that if $A$ is a finite type algebra over a field $k$ then ${\rm Pic}^{\it G}({\it A})$ is contracted in the…

The p-adic Simpson correspondence due to Faltings is a p-adic analogue of non-abelian Hodge theory. The following is the main result of this article: The correspondence for line bundles can be enhanced to a rigid analytic morphism of moduli…

We determined the Picard group of the moduli of rank two stable sheaves on an arbitrary algebraic surface up to finite index

A semialgebraic bijection from the field of p-adic numbers to itself minus one point is constructed. Semialgebraic p-adic sets are classified up to semialgebraic bijection. A cell decomposition theorem for restricted analytic p-adic maps is…

In this paper we generalize work of Amice and Lazard from the early (nineteen) sixties. Amice determined the dual of the space of locally Qp-analytic functions on Zp and showed that it is isomorphic to the ring of rigid functions on the…

In this short note, we show that a natural generalization of the $p$-adic Fourier theory of Schneider and Teitelbaum follows immediately from the classification of $p$-divisible groups over $\cal{O}_{\mathbb{C}_p}$ by Scholze and Weinstein.…

For a connected smooth proper rigid space $X$ over a perfectoid field extension of $\mathbb Q_p$, we show that the \'etale Picard functor of $X$ defined on perfectoid test objects is the diamondification of the rigid analytic Picard…

In their book Rapoport and Zink constructed rigid analytic period spaces for Fontaine's filtered isocrystals, and period morphisms from moduli spaces of p-divisible groups to some of these period spaces. We determine the image of these…

We interpret the structure of the adele class space of the rationals--and specifically its Riemann sector--as the natural monoidal extension of the Picard group of the arithmetic curve $\overline{\operatorname{Spec} \mathbb Z}$. We identify…

Let $G$ be a $p$-adic reductive group and $\mathfrak{g}$ its Lie algebra. We construct a functor from the extension closure of the Bernstein-Gelfand-Gelfand category $\mathcal{O}$ associated to $\mathfrak{g}$ into the category of locally…

A new conjecture on characters of finite groups, related to the McKay conjecture, was proposed recently by the first and third authors. In this paper, we prove it for $p$-solvable groups when $p$ is odd.

This is the second article in a two-part project whose aim is to study algebraic and analytic ranks in $p$-adic families of modular forms. Let $f$ be a newform of weight $2$, square-free level $N$ and trivial character, let $A_f$ be the…

Let $X$ be a smooth and proper scheme over an algebraically closed field. The purpose of the current text is twofold. First, we construct the moduli stack parametrizing rank $n$ continuous $p$-adic representations of the \'etale fundamental…

Sen attached to each p-adic Galois representation of a p-adic field a multiset of numbers called generalized Hodge-Tate weights. In this paper, we discuss a rigidity of these numbers in a geometric family. More precisely, we consider a…

Inspired by several alternative definitions of continued fraction expansions for elements in $\mathbb Q_p$, we study $p$-adically convergent periodic continued fractions with partial quotients in $\mathbb Z[1/p]$. To this end, following a…

For any smooth connected linear algebraic group G over an algebraically closed field k, we describe the Picard group of the universal moduli stack of principal G-bundles over pointed smooth k-projective curves.

We develop an approach to the character theory of certain classes of finite and profinite groups based on the construction of a Lie algebra associated to such a group, but without making use of the notion of a polarization which is central…

We prove a Grothendieck-Lefschetz theorem for equivariant Picard groups of non-singular varieties with finite group actions.

For a linear differential equation defined over a formally real differential field K with real closed field of constants k, Crespo, Hajto and van der Put proved that there exists a unique formally real Picard- Vessiot extension up to…

We study characters of states in $p$-adic vertex operator algebras. In particular, we show that the image of the character map for both the $p$-adic Heisenberg and $p$-adic lattice vertex operator algebras contain infinitely-many…