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Georgios Pappas

Publications and source records attributed to Georgios Pappas.

13 recordsLinked to original sources
arXiv2026

Toric schemes and integral models for Shimura varieties with $\Gamma_1(p)$-type level

We propose a conjectural theory of $p$-integral models of Shimura varieties with level structure at $p$ given by a class of normal subgroups of parahoric subgroups with abelian quotient group. The role of the theory of local models is played in this context by a certain root stack over the local model for parahoric level. The construction of this root stack is based on the "divisor theorem" (a foundational fact about local models) and on the theory of toric varieties in this context, both of which are of independent interest. We prove our conjecture in the case of Shimura varieties of PEL type when the parahoric is an Iwahori (under some additional conditions).

math.AG↗
arXiv2025

p-adic Borel extension for local Shimura varieties

We show that the moduli spaces of Scholze's $p$-adic shtukas with framing satisfy a $p$-adic rigid analytic version of Borel's extension theorem. In particular, this holds for local Shimura varieties, for all local Shimura data $(G,[b],\{\mu\})$, even for exceptional groups $G$, and extends work of Oswal-Shankar-Zhu-Patel who proved a $p$-adic Borel extension property for Rapoport-Zink spaces. As a corollary, we deduce that all these spaces satisfy a $p$-adic rigid analytic version of Brody hyperbolicity.

math.NT↗
arXiv2023

On the smooth locus of affine Schubert varieties

We give a simple and uniform proof of a conjecture of Haines-Richarz characterizing the smooth locus of Schubert varieties in twisted affine Grassmannians. Our method is elementary and avoids any representation theoretic techniques, instead relying on a combinatorial analysis of tangent spaces of Schubert varieties.

math.AG↗
arXiv2022

On tamely ramified $\mathcal G$-bundles on curves

We consider parahoric Bruhat-Tits group schemes over a smooth projective curve and torsors under them. If the characteristic of the ground field is either zero or positive but not too small and the generic fiber is absolutely simple and simply-connected, we show that such group schemes can be written as invariants of reductive group schemes over a tame cover of the curve. We relate the torsors under the Bruhat-Tits group scheme and torsors under the reductive group scheme over the cover which are equivariant for the action of the covering group. For this, we develop a theory of local types for such equivariant torsors. We also relate the moduli stacks of torsors under the Bruhat-Tits group scheme and equivariant torsors under the reductive group scheme over the cover. In an Appendix, B. Conrad provides a proof of the Hasse principle for adjoint groups over function fields with finite field of constants.

math.AG↗
arXiv2022

The Laser Interferometer Space Antenna mission in Greece White Paper

The Laser Interferometer Space Antenna (LISA) mission, scheduled for launch in the mid-2030s, is a gravitational wave observatory in space designed to detect sources emitting in the millihertz band. LISA is an ESA flagship mission, currently entering the Phase B development phase. It is expected to help us improve our understanding about our Universe by measuring gravitational wave sources of different types, with some of the sources being at very high redshifts $z\sim 20$. On the 23rd of February 2022 we organized the 1$^\mathrm{st}$ {\it LISA in Greece Workshop}. This workshop aimed to inform the Greek scientific and tech industry community about the possibilities of participating in LISA science and LISA mission, with the support of the Hellenic Space Center (HSC). In this white paper, we summarize the outcome of the workshop, the most important aspect of it being the inclusion of $15$ Greek researchers to the LISA Consortium, raising our total number to $22$. At the same time, we present a road-map with the future steps and actions of the Greek Gravitational Wave community with respect to the future LISA mission.

gr-qc↗
arXiv2022

On integral local Shimura varieties

We give a construction of "integral local Shimura varieties" which are formal schemes that generalize the well-known integral models of the Drinfeld $p$-adic upper half spaces. The construction applies to all classical groups, at least for odd $p$. These formal schemes also generalize the formal schemes defined by Rapoport-Zink via moduli of $p$-divisible groups, and are characterized purely in group-theoretic terms. More precisely, for a local $p$-adic Shimura datum $(G, b, \mu)$ and a quasi-parahoric group scheme $\mathcal G$ for $G$, Scholze has defined a functor on perfectoid spaces which parametrizes $p$-adic shtukas. He conjectured that this functor is representable by a normal formal scheme which is locally formally of finite type and flat over $O_{\breve E}$. Scholze-Weinstein proved this conjecture when $(G, b, \mu)$ is of (P)EL type by using Rapoport-Zink formal schemes. We prove this conjecture for any $(G, \mu)$ of abelian type when $p\neq 2$, and when $p=2$ and $G$ is of type $A$ or $C$. We also relate the generic fiber of this formal scheme to the local Shimura variety, a rigid-analytic space attached by Scholze to $(G, b, \mu, {\mathcal G})$.

math.AG↗
arXiv2021

Regular integral models for Shimura varieties of orthogonal type

We consider Shimura varieties for orthogonal or spin groups acting on hermitian symmetric domains of type IV. We give regular p-adic integral models for these varieties over odd primes p at which the level subgroup is the connected stabilizer of a vertex lattice in the orthogonal space. Our construction is obtained by combining results of Kisin and the first author with an explicit presentation and resolution of a corresponding local model.

math.NT↗
arXiv2021

Game and Simulation Design for Studying Pedestrian-Automated Vehicle Interactions

The present cross-disciplinary research explores pedestrian-autonomous vehicle interactions in a safe, virtual environment. We first present contemporary tools in the field and then propose the design and development of a new application that facilitates pedestrian point of view research. We conduct a three-step user experience experiment where participants answer questions before and after using the application in various scenarios. Behavioral results in virtuality, especially when there were consequences, tend to simulate real life sufficiently well to make design choices, and we received valuable insights into human/vehicle interaction. Our tool seemed to start raising participant awareness of autonomous vehicles and their capabilities and limitations, which is an important step in overcoming public distrust of AVs. Further, studying how users respect or take advantage of AVs may help inform future operating mode indicator design as well as algorithm biases that might support socially-optimal AV operation.

cs.CY↗
arXiv2021

p-adic shtukas and the theory of global and local Shimura varieties

We establish basic results on p-adic shtukas and apply them to the theory of local and global Shimura varieties, and on their interrelation. We construct canonical integral models for (local, and global) Shimura varieties of Hodge type with parahoric level structure.

math.NT↗
arXiv2019

A gamified simulator and physical platform for self-driving algorithm training and validation

We identify the need for a gamified self-driving simulator where game mechanics encourage high-quality data capture, and design and apply such a simulator to collecting lane-following training data. The resulting synthetic data enables a Convolutional Neural Network (CNN) to drive an in-game vehicle. We simultaneously develop a physical test platform based on a radio-controlled vehicle and the Robotic Operating System (ROS) and successfully transfer the simulation-trained model to the physical domain without modification. The cross-platform simulator facilitates unsupervised crowdsourcing, helping to collect diverse data emulating complex, dynamic environment data, infrequent events, and edge cases. The physical platform provides a low-cost solution for validating simulation-trained models or enabling rapid transfer learning, thereby improving the safety and resilience of self-driving algorithms.

cs.RO↗
arXiv2018

Arithmetic models for Shimura varieties

We describe recent work on the construction of well-behaved arithmetic models for large classes of Shimura varieties and report on progress in the study of these models.

math.NT↗
arXiv2012

Finite Morphisms to Projective Space and Capacity Theory

We study conditions on a commutative ring R which are equivalent to the following requirement; whenever X is a projective scheme over S = Spec(R) of fiber dimension \leq d for some integer d \geq 0, there is a finite morphism from X to P^d_S over S such that the pullbacks of coordinate hyperplanes give prescribed subschemes of X provided these subschemes satisfy certain natural conditions. We use our results to define a new kind of capacity for adelic subsets of projective schemes X over global fields. This capacity can be used to generalize the converse part of the Fekete-Szegő Theorem.

math.AG↗