nLab Rational and p-adic Homotopy Theory

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Jacob Lurie,

DAG XIII: Rational and p-Adic Homotopy Theory

2011

pdf, pdf

on rational homotopy theory and p-adic homotopy theory seen within the theory of algebraic ∞-stacks and derived algebraic geometry.

Contents

Rational homotopy theory
$E_\infty$ -Algebras in positive characteristic

2.1 Norm maps
2.2 Power operations on $E_\infty$ -Algebras
2.3 Finitely constructible sheaves
2.4 A Universal coefficient theorem
2.5 Compactness of relative cochain algebras
2.6 Affine behaviour of $p$ -constructible morphisms

Rational homotopy theory

rational homotopy theory
fundamental theorem of dg-algebraic rational homotopy theory

(Prop. 1.3.3, 1.3.4)

$E_\infty$ -Algebras in positive characteristic

2.1 Norm maps

2.2 Power operations on $E_\infty$ -Algebras

2.3 Finitely constructible sheaves

finitely constructible object

2.4 A Universal coefficient theorem

2.5 Compactness of relative cochain algebras

2.6 Affine behaviour of $p$ -constructible morphisms

category: reference

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