Results 11 to 20 of about 284 (50)
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
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
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
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
Matrices induced by arithmetic functions, primes and groupoid actions of directed graphs
Special Matrices, 2015 In this paper, we study groupoid actions acting on arithmetic functions. In particular, we are interested in the cases where groupoids are generated by directed graphs. By defining an injective map α from the graph groupoid G of a directed graph G to the
Cho Ilwoo, Jorgensen Palle E. T.
doaj +1 more source
Commentary on “Arithmetic on curves” by Barry Mazur
, 2018 Immediately following the commentary below, this previously published article is reprinted in its entirety: B. Mazur, Arithmetic on curves, Bull. Amer. Math. Soc. (N.S.) 14 (1986), no. 2, 207–259.
B. Totaro
semanticscholar +1 more source
A note on the Mumford-Tate Conjecture for CM abelian varieties
, 2014 The Mumford-Tate conjecture is first proved for CM abelian varieties by H. Pohlmann [Ann. Math., 1968]. In this note we give another proof of this result and extend it to CM motives.Comment: 10 pages, to appear in Taiwanese J ...
Yu, Chia-Fu
core +1 more source