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School Colloquium——Stable reduction of algebraic curves and abelian varieties
北大 algebraic curves abelian varieties
2023/6/16
The stable reduction theorem was proved by Grothendieck for Abelian varieties and subsequently by Deligne and Mumford for projective curves.
ESSENTIAL DIMENSION OF ABELIAN VARIETIES OVER NUMBER FIELDS
ESSENTIAL DIMENSION OVER NUMBER FIELDS
2015/9/29
We affirmatively answer a conjecture in the preprint “Essential
dimension and algebraic stacks,” proving that the essential dimension of an
abelian variety over a number field is inʂ...
ABELIAN VARIETIES OVER LARGE ALGEBRAIC FIELDS WITH INFINITE TORSION
ABELIAN VARIETIES OVER LARGE ALGEBRAIC FIELDS INFINITE TORSION
2015/8/26
Let A be a non-zero abelian variety defined over a number field K and let K be a fixed algebraic closure of K. For each element σ of the absolute Galois group Gal(K/K), let K(σ) be the fixed field in ...
HIGHER-LEVEL CANONICAL SUBGROUPS IN ABELIAN VARIETIES
ABELIAN VARIETIES CANONICAL SUBGROUPS
2015/7/6
An abeloid space over a rigid space S over a non-archimedean field k is a proper
smooth S-group A → S with connected fibers. Relative ampleness (in the sense of [C3]) gives a good notion
...
On Colmez's product formula for periods of CM-abelian varieties
Fermat curve stable reduction product formula
2011/7/4
Abstract: Colmez conjectured a product formula for periods of abelian varieties with complex multiplication by a field K, analogous to the standard product formula in algebraic number theory. He prove...
Homomorphisms of abelian varieties over geometric fields of finite characteristic
Homomorphisms of abelian varieties geometric fields of finite characteristic
2010/12/31
We study analogues of Tate’s conjecture on homomorphisms for abelian varieties when the ground field is finitely generated over an algebraic closure of a finite field. Our results cover the case of ab...
Motivic zeta functions for degenerations of abelian varieties and Calabi-Yau varieties
Motivic zeta functions degenerations of abelian varieties Calabi-Yau varieties
2010/12/31
Let f ∈ Z[x1, . . . , xn] be a non-constant polynomial, and let p be a prime. Igusa’s p-adic zeta function Zp f (s) is a meromorphic function on the complex plane that encodes the number of solutions ...
Artin representations attached to pairs of isogenous abelian varieties
Artin representations pairs of isogenous abelian varieties
2010/12/16
Given a pair of abelian varieties defined over a number field k and isogenous over a finite Galois extension L/k, we define a rational Artin representation of the group Gal(L/k) that shows a global re...
On The Characteristic Polynomial of Frobenius of Supersingular Abelian Varieties Of Dimension up to 7 over Finite Fields
The Characteristic Polynomial Frobenius Supersingular Abelian
2010/11/1
In this article, we derive the list of the characteristic polynomials of the Frobenius endomorphism of simple supersingular abelian varieties of dimension $1,~2,~3,~4,~5,~6,~7$ over $\mathbb{F}_q$ whe...
A Grunwald-Wang type theorem for abelian varieties
Grunwald-Wang type theorem abelian varieties
2010/10/15
Let A be an abelian variety over a number field k. We show that weak approxima-tion holds in the Weil-Chˆatelet group, H1(k,A), but that it may fail when one restricts to the n-torsion subgroup.
We prove a strong form of the motivic monodromy conjecture for abelian varieties, by showing that the order of the unique pole of the motivic zeta function is equal to the size of the maximal Jordan b...