Results 11 to 20 of about 264 (44)
Pink's conjecture on unlikely intersections and families of semi-abelian varieties [PDF]
, 2020 The Poincar\'e torsor of a Shimura family of abelian varieties can be viewed both as a family of semi-abelian varieties and as a mixed Shimura variety.
Bertrand, Daniel, Edixhoven, Bas
core +3 more sources
Constructing elliptic curves of prime order [PDF]
, 2007 We present a very efficient algorithm to construct an elliptic curve E and a finite field F such that the order of the point group E(F) is a given prime number N.
Broker, Reinier, Stevenhagen, Peter
core +3 more sources
The p-torsion of curves with large p-rank [PDF]
, 2008 Consider the locus of smooth curves of genus g and p-rank f defined over an algebraically closed field k of characteristic p. It is an open problem to classify which group schemes occur as the p-torsion of the Jacobians of these curves for f < g-1.
Pries, Rachel
core +4 more sources
Definite orders with locally free cancellation
Transactions of the London Mathematical Society, Volume 6, Issue 1, Page 53-86, December 2019., 2019 Abstract We enumerate all orders in definite quaternion algebras over number fields with the Hermite property; this includes all orders with the cancellation property for locally free modules.
Daniel Smertnig, John Voight
wiley +1 more source
Remark on the rank of elliptic curves [PDF]
, 2009 A covariant functor on the elliptic curves with complex multiplication is constructed. The functor takes values in the noncommutative tori with real multiplication. A conjecture on the rank of an elliptic curve is formulated.Comment: 13 pages, 2 figures;
Nikolaev, Igor
core +3 more sources
Krein-space operators determined by free product algebras induced by primes and graphs
Special Matrices, 2017 In this paper, we introduce certain Krein-space operators induced by free product algebras induced by both primes and directed graphs. We study operator-theoretic properties of such operators by computing free-probabilistic data containing number ...
Cho Ilwoo, Jorgensen Palle E. T.
doaj +1 more source
COMPACTIFICATIONS OF PEL-TYPE SHIMURA VARIETIES IN RAMIFIED CHARACTERISTICS
Forum of Mathematics, Sigma, 2016 We show that, by taking normalizations over certain auxiliary good reduction integral models, one obtains integral models of toroidal and minimal compactifications of PEL-type Shimura varieties which enjoy many features of the good reduction theory ...
KAI-WEN LAN
doaj +1 more source
Open Mathematics, 2019 After the significant work of Zagier on the traces of singular moduli, Jeon, Kang and Kim showed that the Galois traces of real-valued class invariants given in terms of the singular values of the classical Weber functions can be identified with the ...
Eum Ick Sun, Jung Ho Yun
doaj +1 more source
COMPACTIFICATIONS OF SUBSCHEMES OF INTEGRAL MODELS OF SHIMURA VARIETIES
Forum of Mathematics, Sigma, 2018 We study several kinds of subschemes of mixed characteristic models of Shimura varieties which admit good (partial) toroidal and minimal compactifications, with familiar boundary stratifications and formal local structures, as if they were Shimura ...
KAI-WEN LAN, BENOÎT STROH
doaj +1 more source
Supercongruences and Complex Multiplication [PDF]
, 2012 We study congruences involving truncated hypergeometric series of the form_rF_{r-1}(1/2,...,1/2;1,...,1;\lambda)_{(mp^s-1)/2} = \sum_{k=0}^{(mp^s-1)/2} ((1/2)_k/k!)^r \lambda^k where p is a prime and m, s, r are positive integers.
Kibelbek, Jonas +4 more
core +1 more source