arXiv subjects

David-Alexandre Guiraud

Publications and source records attributed to David-Alexandre Guiraud.

4 recordsLinked to original sources

arXiv2025

Objectives and Design Principles in Offline Payments with Central Bank Digital Currency (CBDC)

In this work, fundamental design principles for a central bank digital currency (CBDC) with an offline functionality and corresponding counter measures are discussed. We identify three major objectives for any such CBDC proposal:(i) Access Control Security - protection of a user's funds against unauthorized access by other users; (ii) Security against Depositor's Misbehavior - preservation of the integrity of an environment (potentially the wallet) against misbehavior of its owner (for example, double-spending), and (iii) Privacy by Design - ensuring privacy is embedded into the system architecture. Our central conclusion is the alignment of the objectives to concrete design elements as countermeasures, whereas certain objectives and countermeasures have no or minimal interferences with each other. For example, we work out that the integrity of a user's wallet and, accordingly, the prevention of double-spending race attacks should be addressed through the adoption and integration of \textit{secure hardware} within a CBDC system.

cs.CR↗

arXiv2018

Unobstructedness of Galois deformation rings associated to RACSDC automorphic representations

Let $F$ be a CM field and let $(\overline{r}_{π,λ})_λ$ be the compatible system of residual $\mathcal{G}_n$-valued representations of $\operatorname{Gal}_{F}$ attached to a RACSDC automorphic representation $π$ of $\operatorname{GL}_n(\mathbb{A})$, as studied by Clozel, Harris and Taylor and others. Under mild assumptions, we prove that the fixed-determinant universal deformation rings attached to $\overline{r}_{π,λ}$ are unobstructed for all places $λ$ in a subset of Dirichlet density $1$, continuing the investigations of Mazur, Weston and Gamzon. During the proof, we develop a general framework for proving unobstructedness (which could be useful for other applications in future) and an $R=T$-theorem, relating the universal crystalline deformation ring of $\overline{r}_{π,λ}$ and a certain unitary fixed-type Hecke algebra.

math.NT↗

arXiv2014

Functional Hecke algebras and simple Bernstein blocks of a p-adic GL_n in non-defining characteristic

Let $G_{n}=\operatorname{GL}_{n}(F)$, where $F$ is a non-archimedean local field with residue characteristic $p$ and where $n=2k$ is even. In this article, we investigate a question occurring in the decomposition of the category of $\ell$-modular smooth representations of $G_n$ into Bernstein blocks (where $\ell\neq p$). The easiest block not investigated in \cite{guiraud} is the one defined by the standard parabolic subgroup with Levi factor $M=\GL_k(F) \times \GL_k(F)$ and by an $M$-representation of the form $π_0 \boxtimes π_0$ with $π_0$ a supercuspidal $\GL_k(F)$-representation. This block is Morita equivalent to a Hecke algebra which we can describe as a twisted tensor product of a finite Hecke algebra (i. e. a Hecke algebra occurring in the representation theory of the finite group $\GL_k(p^α)$ in non-defining characteristic $\ell$) and the group ring of $\mathbb{Z}^2$. This enables us to describe how a conjectured connection between finite Hecke algebras (which is similar to a connection postulated by Broué in \cite{Broue}) would lead to an equivalence between the described block and the unipotent block of $\operatorname{GL}_2(F^k)$, where $F^k$ is the unramified extension of degree $k$ over $F$.

math.NT↗

arXiv2011

On semisimple l-modular Bernstein-blocks of a p-adic general linear group

Let $G_n=\operatorname{GL}_n(F)$, where $F$ is a non-archimedean local field with residue characteristic $p$. Our starting point is the Bernstein-decomposition of the representation category of $G_n$ over an algebraically closed field of characteristic $\ell \neq p$ into blocks. In level zero, we associate to each block a replacement for the Iwahori-Hecke algebra which provides a Morita-equivalence just as in the complex case. Additionally, we will explain how this gives rise to a description of an arbitrary $G_n$-block in terms of simple $G_m$-blocks (for $m\leq n$), paralleling the approach of Bushnell and Kutzko in the complex setting.

math.RT↗