Results 11 to 20 of about 43,119 (196)
Abelian varieties over fields of finite characteristic
Open Mathematics, 2014 Zarhin Yuri
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Logarithmic Abelian Varieties [PDF]
Nagoya Mathematical Journal, 2008 AbstractWe develop the algebraic theory of log abelian varieties. This is Part II of our series of papers on log abelian varieties, and is an algebraic counterpart of the previous Part I ([6]), where we developed the analytic theory of log abelian varieties.
Kajiwara, Takeshi +2 more
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Nagoya Mathematical Journal, 1953 In a Bourbaki seminary note, La Théorie des Fonctions Thêta, A. Weil has discussed two fundamental theorems of the general theory of Theta functions. The first, due to H. Poincaré, was proved very skilfully in the note by means of harmonic integrals on a torus and the second, due to Frobenius, was treated by the systematic use of the notion of analytic
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The effective Shafarevich conjecture for abelian varieties of ${\text {GL}_{2}}$-type
Forum of Mathematics, Sigma, 2021 In this article we establish the effective Shafarevich conjecture for abelian varieties over ${\mathbb Q}$ of ${\text {GL}_2}$-type. The proof combines Faltings’ method with Serre’s modularity conjecture, isogeny estimates and results from Arakelov ...
Rafael von Känel
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Degenerating abelian varieties via log abelian varieties [PDF]
Asian Journal of Mathematics, 2018 For any split totally degenerate abelian variety over a complete discrete valuation field, we construct a log abelian variety over the discrete valuation ring extending the given abelian variety. This generalizes the log Tate curve of Kato.
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Finite $F$-representation type for homogeneous coordinate rings of non-Fano varieties [PDF]
Épijournal de Géométrie Algébrique, 2023 Finite $F$-representation type is an important notion in characteristic-$p$ commutative algebra, but explicit examples of varieties with or without this property are few.
Devlin Mallory
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SINGULARITIES OF THE BIEXTENSION METRIC FOR FAMILIES OF ABELIAN VARIETIES
Forum of Mathematics, Sigma, 2018 In this paper we study the singularities of the invariant metric of the Poincaré bundle over a family of abelian varieties and their duals over a base of arbitrary dimension.
JOSÉ IGNACIO BURGOS GIL +2 more
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Super-isolated abelian varieties [PDF]
Journal of Number Theory, 2020 We call an abelian variety over a finite field $\mathbb{F}_q$ super-isolated if its ($\mathbb{F}_q$-rational) isogeny class contains a single isomorphism class. In this paper, we use the Honda-Tate theorem to characterize super-isolated ordinary simple abelian varieties by certain algebraic integers.
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Rationally connected rational double covers of primitive Fano varieties [PDF]
Épijournal de Géométrie Algébrique, 2020 We show that for a Zariski general hypersurface $V$ of degree $M+1$ in ${\mathbb P}^{M+1}$ for $M\geqslant 5$ there are no Galois rational covers $X\dashrightarrow V$ of degree $d\geqslant 2$ with an abelian Galois group, where $X$ is a rationally ...
Aleksandr V. Pukhlikov
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Characterization of abelian varieties [PDF]
Inventiones Mathematicae, 2001 10 pages ...
Chen, J.A., Hacon, C.D.
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