van Hoeij, Mark Smith, Hanson
Published in
Research in Number Theory

We give a formula for divisors of modular units on X1(N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$X_1(N)$$\end{document} and use it to prove that the Q\documentcl...

三枝, 洋一

"Algebraic Number Theory and Related Topics 2016". November 28 - December 2, 2016. edited by Yasuo Ohno, Hiroshi Tsunogai and Toshiro Hiranouchi. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. / This is a survey article on Arthur's conjectural classification of automorphic representations of connected...

Daw, Christopher Javanpeykar, Ariyan Kühne, Lars
Published in
Selecta Mathematica

Let Z be an algebraic subvariety of a Shimura variety. We extend results of the first author to prove an effective upper bound for the degree of a non-facteur maximal special subvariety of Z.

Rivero, Óscar Rotger, Victor
Published in
Forum Mathematicum

We study weight one specializations of the Euler system of Beilinson–Flach elements introduced by Kings, Loeffler and Zerbes, with a view towards a conjecture of Darmon, Lauder and Rotger relating logarithms of units in suitable number fields to special values of the Hida–Rankin p-adic L-function. We show that the latter conjecture follows from exp...

Howard, Benjamin
Published in
Forum Mathematicum

We prove an invariance property of intersections of Kudla–Rapoport divisors on a unitary Rapoport–Zink space.

Longo, Matteo Nicole, Marc-Hubert
Published in
Forum Mathematicum

We relate p-adic families of Jacobi forms to big Heegner points constructed by B. Howard, in the spirit of the Gross–Kohnen–Zagier theorem. We view this as a GL ( 2 ) {\mathrm{GL}(2)} instance of a p-adic Kudla program.

Koskivirta, Jean-Stefan
Published in
Results in Mathematics

We define automorphic vector bundles on the stack of G-zips introduced by Moonen–Pink–Wedhorn–Ziegler and study their global sections. In particular, we give a combinatorial condition on the weight for the existence of nonzero mod p automorphic forms on Shimura varieties of Hodge-type. We attach to the highest weight of the representation V(λ)\docu...

Baldi, Gregorio
Published in
Archiv der Mathematik

Recently S. Patrikis, J.F. Voloch, and Y. Zarhin have proven, assuming several well-known conjectures, that the finite descent obstruction holds on the moduli space of principally polarised abelian varieties. We show an analogous result for K3 surfaces, under some technical restrictions on the Picard rank. This is possible since abelian varieties a...

Wei, Fu-Tsun Yamazaki, Takao
Published in
Forum Mathematicum

We consider the generalized Jacobian J ~ {\widetilde{J}} of the modular curve X 0 ( N ) {X_{0}(N)} of level N with respect to a reduced divisor consisting of all cusps. Supposing N is square free, we explicitly determine the structure of the ℚ {\mathbb{Q}} -rational torsion points on J ~ {\widetilde{J}} up to 6-primary torsion. The result depicts...

Li, Wanlin Mantovan, Elena Pries, Rachel Tang, Yunqing
Published in
Research in Number Theory

By a result of Moonen, there are exactly 20 positive-dimensional families of cyclic covers of the projective line for which the Torelli image is open and dense in the associated Shimura variety. For each of these, we compute the Newton polygons, and the μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \...