The Tate conjecture for K3 surfaces—a survey of some recent progress

2014 ◽  
Vol 39 (1) ◽  
pp. 69-85
Author(s):  
Vasudevan Srinivas
Keyword(s):  
Recent Progress ◽  
K3 Surfaces ◽  
Tate Conjecture

scholarly journals Integral canonical models for Spin Shimura varieties

2015 ◽  
Vol 152 (4) ◽  
pp. 769-824 ◽  
Author(s):  
Keerthi Madapusi Pera
Keyword(s):  
Modular Forms ◽  
Fourier Coefficients ◽  
K3 Surfaces ◽  
Shimura Varieties ◽  
Good Reduction ◽  
Intersection Numbers ◽  
Orthogonal Groups ◽  
Canonical Models ◽  
Tate Conjecture ◽  
Precise Sense

We construct regular integral canonical models for Shimura varieties attached to Spin and orthogonal groups at (possibly ramified) primes$p>2$where the level is not divisible by$p$. We exhibit these models as schemes of ‘relative PEL type’ over integral canonical models of larger Spin Shimura varieties with good reduction at$p$. Work of Vasiu–Zink then shows that the classical Kuga–Satake construction extends over the integral models and that the integral models we construct are canonical in a very precise sense. Our results have applications to the Tate conjecture for K3 surfaces, as well as to Kudla’s program of relating intersection numbers of special cycles on orthogonal Shimura varieties to Fourier coefficients of modular forms.

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

scholarly journals The Tate conjecture for K3 surfaces in odd characteristic

2014 ◽  
Vol 201 (2) ◽  
pp. 625-668 ◽  
Author(s):  
Keerthi Madapusi Pera
Keyword(s):  
K3 Surfaces ◽  
Tate Conjecture

scholarly journals Finiteness of K3 surfaces and the Tate conjecture

2014 ◽  
Vol 47 (2) ◽  
pp. 285-308 ◽  
Author(s):  
Max Lieblich ◽  
Davesh Maulik ◽  
Andrew Snowden
Keyword(s):  
K3 Surfaces ◽  
Tate Conjecture

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

scholarly journals Recent progress on the Tate conjecture

2017 ◽  
Vol 54 (4) ◽  
pp. 575-590 ◽  
Author(s):  
Burt Totaro
Keyword(s):  
Recent Progress ◽  
Tate Conjecture
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