The Torelli Theorem for Ordinary K3 Surfaces over Finite Fields

1983 ◽  
pp. 267-276
Author(s):  
Niels O. Nygaard
Keyword(s):  
Finite Fields ◽  
K3 Surfaces ◽  
Torelli Theorem

scholarly journals Point counting on K3 surfaces and an application concerning real and complex multiplication

2016 ◽  
Vol 19 (A) ◽  
pp. 12-28 ◽  
Author(s):  
Andreas-Stephan Elsenhans ◽  
Jörg Jahnel
Keyword(s):  
Finite Fields ◽  
Efficient Method ◽  
Complex Multiplication ◽  
K3 Surfaces ◽  
Point Counting

We report on our project to find explicit examples of K3 surfaces having real or complex multiplication. Our strategy is to search through the arithmetic consequences of RM and CM. In order to do this, an efficient method is needed for point counting on surfaces defined over finite fields. For this, we describe algorithms that are$p$-adic in nature.

The Tate conjecture for ordinary K3 surfaces over finite fields

1983 ◽  
Vol 74 (2) ◽  
pp. 213-237 ◽  
Author(s):  
N. O. Nygaard
Keyword(s):  
Finite Fields ◽  
K3 Surfaces ◽  
Tate Conjecture

Transcendental cycles on ordinary $K3$ surfaces over finite fields

1993 ◽  
Vol 72 (1) ◽  
pp. 65-83 ◽  
Author(s):  
Yuri G. Zarhin
Keyword(s):  
Finite Fields ◽  
K3 Surfaces

A New Proof of the Global Torelli Theorem for K3 Surfaces

1984 ◽  
Vol 120 (2) ◽  
pp. 237 ◽  
Author(s):  
Robert Friedman
Keyword(s):  
K3 Surfaces ◽  
Torelli Theorem

K3 Surfaces

2007 ◽  
Author(s):  
D. Huybrechts
Keyword(s):  
Moduli Spaces ◽  
Special Class ◽  
K3 Surfaces ◽  
Derived Categories ◽  
K3 Surface ◽  
Hodge Structures ◽  
Surface Theory ◽  
Torelli Theorem ◽  
Stable Sheaves ◽  
Moduli Theory

After abelian varieties, K3 surfaces are the second most interesting special class of varieties. These have a rich internal geometry and a highly interesting moduli theory. Paralleling the famous Torelli theorem, results from Mukai and Orlov show that two K3 surfaces have equivalent derived categories precisely when their cohomologies are isomorphic weighing two Hodge structures. Their techniques also give an almost complete description of the cohomological action of the group of autoequivalences of the derived category of a K3 surface. The basic definitions and fundamental facts from K3 surface theory are recalled. As moduli spaces of stable sheaves on K3 surfaces are crucial for the argument, a brief outline of their theory is presented.

scholarly journals A Torelli Theorem for Curves over Finite Fields

2010 ◽  
Vol 6 (1) ◽  
pp. 245-294 ◽  
Author(s):  
Fedor Bogomolov ◽  
Mikhail Korotiaev ◽  
Yuri Tschinkel
Keyword(s):  
Finite Fields ◽  
Torelli Theorem ◽  
Curves Over Finite Fields

scholarly journals GENERALIZED CALABI–YAU STRUCTURES, K3 SURFACES, AND B-FIELDS

2005 ◽  
Vol 16 (01) ◽  
pp. 13-36 ◽  
Author(s):  
DANIEL HUYBRECHTS
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Symplectic Form ◽  
Weak Form ◽  
K3 Surfaces ◽  
Standard Theory ◽  
General Notion ◽  
Symplectic Structures ◽  
Special Cases ◽  
Torelli Theorem

Generalized Calabi–Yau structures, a notion recently introduced by Hitchin, are studied in the case of K3 surfaces. We show how they are related to the classical theory of K3 surfaces and to moduli spaces of certain SCFT as studied by Aspinwall and Morrison. It turns out that K3 surfaces and symplectic structures are both special cases of this general notion. The moduli space of generalized Calabi–Yau structures admits a canonical symplectic form with respect to which the moduli space of symplectic structures is Lagrangian. The standard theory of K3 surfaces implies surjectivity of the period map and a weak form of the Global Torelli theorem.

scholarly journals The Tate conjecture for K3 surfaces over finite fields

2012 ◽  
Vol 194 (1) ◽  
pp. 119-145 ◽  
Author(s):  
François Charles
Keyword(s):  
Finite Fields ◽  
K3 Surfaces ◽  
Tate Conjecture
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