scholarly journals Odd order obstructions to the Hasse principle on general K3 surfaces

2019 ◽  
Vol 89 (323) ◽  
pp. 1395-1416
Author(s):  
Jennifer Berg ◽  
Anthony Várilly-Alvarado
Keyword(s):  
K3 Surfaces ◽  
Hasse Principle ◽  
Odd Order

scholarly journals On the Frequency of Algebraic Brauer Classes on Certain Log K3 Surfaces

2018 ◽  
Vol 62 (3) ◽  
pp. 551-563
Author(s):  
Jörg Jahnel ◽  
Damaris Schindler
Keyword(s):  
K3 Surfaces ◽  
Upper Bounds ◽  
Hasse Principle ◽  
Brauer Group ◽  
Integral Points ◽  
Quadratic Equations

AbstractGiven systems of two (inhomogeneous) quadratic equations in four variables, it is known that the Hasse principle for integral points may fail. Sometimes this failure can be explained by some integral Brauer–Manin obstruction. We study the existence of a non-trivial algebraic part of the Brauer group for a family of such systems and show that the failure of the integral Hasse principle due to an algebraic Brauer–Manin obstruction is rare, as for a generic choice of a system the algebraic part of the Brauer-group is trivial. We use resolvent constructions to give quantitative upper bounds on the number of exceptions.

scholarly journals On large Picard groups and the Hasse Principle for curves and K3 surfaces

1996 ◽  
Vol 76 (2) ◽  
pp. 165-189 ◽  
Author(s):  
Daniel Coray ◽  
Constantin Manoil
Keyword(s):  
K3 Surfaces ◽  
Hasse Principle ◽  
Picard Groups

ON FINITE p-GROUPS OF ODD ORDER WITH MANY SUBGROUPS 2-SUBNORMAL

1996 ◽  
Vol 24 (8) ◽  
pp. 2707-2719
Author(s):  
Gemma Parmeggiani ◽  
G. Zacher
Keyword(s):  
Odd Order

A CHARACTERISATION OF CERTAIN FINITE GROUPS OF ODD ORDER

2011 ◽  
Vol 111 (-1) ◽  
pp. 67-76
Author(s):  
Ashish Kumar Das ◽  
Rajat Kanti Nath
Keyword(s):  
Finite Groups ◽  
Odd Order

scholarly journals Motivic integral of K3 surfaces over a non-archimedean field

2011 ◽  
Vol 228 (5) ◽  
pp. 2688-2730 ◽  
Author(s):  
Allen J. Stewart ◽  
Vadim Vologodsky
Keyword(s):  
K3 Surfaces

scholarly journals Verlinde formulae on complex surfaces: K-theoretic invariants

2021 ◽  
Vol 9 ◽  
Author(s):  
L. Göttsche ◽  
M. Kool ◽  
R. A. Williams
Keyword(s):  
Moduli Space ◽  
K3 Surfaces ◽  
Complex Surfaces ◽  
Type Formula ◽  
Verlinde Formula ◽  
Donaldson Invariants

Abstract We conjecture a Verlinde type formula for the moduli space of Higgs sheaves on a surface with a holomorphic 2-form. The conjecture specializes to a Verlinde formula for the moduli space of sheaves. Our formula interpolates between K-theoretic Donaldson invariants studied by Göttsche and Nakajima-Yoshioka and K-theoretic Vafa-Witten invariants introduced by Thomas and also studied by Göttsche and Kool. We verify our conjectures in many examples (for example, on K3 surfaces).

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