On two theorems for flat, affine group schemes over a discrete valuation ring [PDF]
Open Mathematics, 2005 We include short and elementary proofs of two theorems characterizing reductive group schemes over a discrete valuation ring, in a slightly more general context.Comment: 10 pages. To appear in C. E. J.
Vasiu Adrian
doaj +2 more sources
THE SHIMURA CURVE OF DISCRIMINANT 15 AND TOPOLOGICAL AUTOMORPHIC FORMS [PDF]
Forum of Mathematics, Sigma, 2015 We find defining equations for the Shimura curve of discriminant 15 over $\mathbb{Z}[1/15]$. We then determine the graded ring of automorphic forms over the 2-adic integers, as well as the higher cohomology. We apply this to calculate the homotopy groups
TYLER LAWSON
doaj +5 more sources
Automorphic vector bundles on the stack of G-zips
Forum of Mathematics, Sigma, 2021 For a connected reductive group G over a finite field, we study automorphic vector bundles on the stack of G-zips. In particular, we give a formula in the general case for the space of global sections of an automorphic vector bundle in terms of the ...
Naoki Imai, Jean-Stefan Koskivirta
doaj +1 more source
CM liftings of $K3$ surfaces over finite fields and their applications to the Tate conjecture
Forum of Mathematics, Sigma, 2021 We give applications of integral canonical models of orthogonal Shimura varieties and the Kuga-Satake morphism to the arithmetic of $K3$ surfaces over finite fields.
Kazuhiro Ito +2 more
doaj +1 more source
Point counting for foliations over number fields
Forum of Mathematics, Pi, 2022 Let${\mathbb M}$ be an affine variety equipped with a foliation, both defined over a number field ${\mathbb K}$. For an algebraic $V\subset {\mathbb M}$ over ${\mathbb K}$, write $\delta _{V}$ for the maximum of the degree and log-height of V.
Gal Binyamini
doaj +1 more source
A Mordell-Weil theorem for cubic hypersurfaces of high dimension [PDF]
, 2016 Let $X$ be a smooth cubic hypersurface of dimension $n \ge 1$ over the rationals. It is well-known that new rational points may be obtained from old ones by secant and tangent constructions.
Papanikolopoulos, Stefanos +1 more
core +2 more sources
On Artin representations and nearly ordinary Hecke algebras over totally real fields
Documenta Mathematica, 2013 We prove many new cases of the strong Artin conjecture for two-dimensional, totally odd, insoluble (icosahedral) representations Gal(F/F ) → GL2(C) of the absolute Galois group of a totally real field F .
Shu Sasaki
semanticscholar +1 more source
The EKOR-stratification on the Siegel modular variety with parahoric level structure [PDF]
Épijournal de Géométrie AlgébriqueWe study the arithmetic geometry of the reduction modulo $p$ of the Siegel modular variety with parahoric level structure. We realize the EKOR-stratification on this variety as the fibers of a smooth morphism into an algebraic stack parametrizing ...
Manuel Hoff
doaj +1 more source
Several variables $p$-adic $L$-functions for Hida families of Hilbert modular forms
Documenta Mathematica, 2012 After formulating Conjecture A for p-adic L-functions defined over ordinary Hilbert modular Hida deformations on a totally real field F of degree d, we construct two p-adic L-functions of d+1-variable depending on the parity of weight as a partial result
T. Ochiai
semanticscholar +1 more source
ENLARGED MIXED SHIMURA VARIETIES, BI-ALGEBRAIC SYSTEM AND SOME AX TYPE TRANSCENDENTAL RESULTS
Forum of Mathematics, Sigma, 2019 We develop a theory of enlarged mixed Shimura varieties, putting the universal vectorial bi-extension defined by Coleman into this framework to study some functional transcendental results of Ax type. We study their bi-algebraic systems, formulate the Ax-
ZIYANG GAO
doaj +1 more source