Results 11 to 20 of about 515 (46)

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

On component groups of Jacobians of quaternionic modular curves [PDF]

, 2016
We use a combinatorial result relating the discriminant of the cycle pairing on a weighted finite graph to the eigenvalues of its Laplacian to deduce a formula for the orders of component groups of Jacobians of modular curves arising from quaternion ...
Papikian, Mihran
core   +2 more sources

Monodromy of the p-rank strata of the moduli space of curves [PDF]

, 2007
We compute the Z/\ell and \ell-adic monodromy of every irreducible component of the moduli space M_g^f of curves of genus and and p-rank f. In particular, we prove that the Z/\ell-monodromy of every component of M_g^f is the symplectic group Sp_{2g}(Z ...
Achter, Jeff, Pries, Rachel
core   +5 more sources

Quadratic Points on Modular Curves [PDF]

, 2018
In this paper we determine the quadratic points on the modular curves X_0(N), where the curve is non-hyperelliptic, the genus is 3, 4 or 5, and the Mordell--Weil group of J_0(N) is finite.
Ozman, Ekin, Siksek, Samir
core   +2 more sources

Rational torsion points on Jacobians of modular curves

, 2015
Let $p$ be a prime greater than 3. Consider the modular curve $X_0(3p)$ over $\mathbb{Q}$ and its Jacobian variety $J_0(3p)$ over $\mathbb{Q}$. Let $\mathcal{T}(3p)$ and $\mathcal{C}(3p)$ be the group of rational torsion points on $J_0(3p)$ and the ...
Yoo, Hwajong
core   +1 more source

Gonality of modular curves in characteristic p

, 2006
Let k be an algebraically closed field of characteristic p. Let X(p^e;N) be the curve parameterizing elliptic curves with full level N structure (where p does not divide N) and full level p^e Igusa structure. By modular curve, we mean a quotient of any X(
Poonen, Bjorn
core   +1 more source

2-ADIC INTEGRAL CANONICAL MODELS

Forum of Mathematics, Sigma, 2016
We use Lau’s classification of 2-divisible groups using Dieudonné displays to construct integral canonical models for Shimura varieties of abelian type at 2-adic places where the level is hyperspecial.
WANSU KIM, KEERTHI MADAPUSI PERA
doaj   +1 more source

F-zips with additional structure on splitting models of Shimura varieties

Forum of Mathematics, Sigma
We construct universal G-zips on good reductions of the Pappas-Rapoport splitting models for PEL-type Shimura varieties. We study the induced Ekedahl-Oort stratification, which sheds new light on the mod p geometry of splitting models.
Xu Shen, Yuqiang Zheng
doaj   +1 more source

RAPOPORT–ZINK UNIFORMIZATION OF HODGE-TYPE SHIMURA VARIETIES

Forum of Mathematics, Sigma, 2018
We show that the integral canonical models of Hodge-type Shimura varieties at odd good reduction primes admits ‘$p$-adic uniformization’ by Rapoport–Zink spaces of Hodge type constructed in Kim [Forum Math. Sigma6 (2018) e8, 110 MR 3812116].
WANSU KIM
doaj   +1 more source

FINE DELIGNE–LUSZTIG VARIETIES AND ARITHMETIC FUNDAMENTAL LEMMAS

Forum of Mathematics, Sigma, 2019
We prove a character formula for some closed fine Deligne–Lusztig varieties. We apply it to compute fixed points for fine Deligne–Lusztig varieties arising from the basic loci of Shimura varieties of Coxeter type.
XUHUA HE, CHAO LI, YIHANG ZHU
doaj   +1 more source