\(K3\) surfaces over finite fields with given \(L\)-function

DOI10.2140/ANT.2016.10.1133zbMath1344.14024arXiv1507.08547OpenAlexW3106399383MaRDI QIDQ738834

Lenny Taelman

Publication date: 16 August 2016

Published in: Algebra \& Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.08547

zbMATH Keywords

finite fields\(L\)-functions\(K3\) surfaceszeta functions

Mathematics Subject Classification ID

(K3) surfaces and Enriques surfaces (14J28) Finite ground fields in algebraic geometry (14G15) Complex multiplication and abelian varieties (14K22) Varieties over finite and local fields (11G25)

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Unconditional construction of \(K3\) surfaces over finite fields with given \(L\)-function in large characteristic ⋮ \(W = 0\) complex structure moduli stabilization on CM-type \(\mathrm{K}3 \times \mathrm{K}3\) orbifolds: arithmetic, geometry and particle physics ⋮ Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in \(p\)-adic cohomology ⋮ Finiteness theorems for K3 surfaces and abelian varieties of CM type ⋮ Varieties over finite fields: quantitative theory ⋮ Complex multiplication and Brauer groups of \(K3\) surfaces ⋮ On derived equivalences of \(K3\) surfaces in positive characteristic ⋮ CM liftings of surfaces over finite fields and their applications to the Tate conjecture ⋮ Fields of definition of \(K3\) surfaces with complex multiplication

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