Homotopy theory and arithmetic geometry -- motivic and Diophantine aspects: an introduction
DOI10.1007/978-3-030-78977-0_1zbMath1478.14004OpenAlexW3203467119MaRDI QIDQ2074092
Publication date: 4 February 2022
Full work available at URL: https://doi.org/10.1007/978-3-030-78977-0_1
Degree, winding number (55M25) Étale and other Grothendieck topologies and (co)homologies (14F20) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry (14-01) Homotopy theory and fundamental groups in algebraic geometry (14F35) Arithmetic problems in algebraic geometry; Diophantine geometry (14Gxx) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory (11-01) Motivic cohomology; motivic homotopy theory (14F42) Algebraic cycles and motivic cohomology ((K)-theoretic aspects) (19E15) Arithmetic algebraic geometry (Diophantine geometry) (11Gxx) Cycles and subschemes (14Cxx)
Uses Software
Cites Work
- Anabelian geometry with étale homotopy types
- \(\mathbb A^1\)-algebraic topology over a field
- A quadratic refinement of the Grothendieck-Lefschetz-Verdier trace formula
- Étale homotopy types of moduli stacks of polarised abelian schemes
- Pro-categories in homotopy theory
- Smooth varieties up to \(\mathbb A^1\)-homotopy and algebraic \(h\)-cobordisms
- Homotopical algebraic geometry. I: Topos theory
- Motivic homotopy theory. Lectures at a summer school in Nordfjordeid, Norway, August 2002
- \(p\)-adic étale cohomology
- \(\mathbb{A}^1\)-homotopy theory
- Seminaire de géométrie algébrique du Bois-Marie 1965-66 SGA 5 dirige par A. Grothendieck avec la collaboration de I. Bucur, C. Houzel, L. Illusie, J.-P. Jouanolou et J. -P. Serre. Cohomologie \(\ell\)-adique et fonctions L
- An algebraic formula for the degree of a \(C^\infty\) map germ. Sur une inegalite a la Minkowski pour les multiplicites
- The first stable homotopy groups of motivic spheres
- The class of Eisenbud-Khimshiashvili-Levine is the local \(\mathbb{A}^1\)-Brouwer degree
- Reduced power operations in motivic cohomology
- Motivic cohomology with \(\mathbb Z/2\)-coefficients
- Homology of schemes
- Applications to \(\mathbb{A}^1\)-enumerative geometry of the \(\mathbb{A}^1\)-degree
- Aspects of enumerative geometry with quadratic forms
- Borel-Moore homology, Riemann-Roch transformations, and local terms
- Splitting varieties for triple Massey products
- Étale homotopy equivalence of rational points on algebraic varieties
- Intrinsic signs and lower bounds in real algebraic geometry
- Etale homotopy
- Algebraic \(K\)-theory and quadratic forms. With an appendix by J. Tate
- The motivic fundamental group of \(\mathbf P^1\setminus\{0,1,\infty\}\) and the theorem of Siegel
- Motivic cohomology, localized Chern classes, and local terms
- A projective model structure on pro-simplicial sheaves, and the relative étale homotopy type
- Cobordisme algébrique I
- 3264 and All That
- Étale motives
- Birational invariants and 𝔸1-connectedness
- Weights for Relative Motives: Relation with Mixed Complexes of Sheaves
- Comparing Euler Classes
- Motivic Donaldson-Thomas invariants: summary of results
- Lectures on quadratic enumerative geometry
- Oriented Schubert calculus in Chow–Witt rings of Grassmannians
- Etale Homotopy of Simplicial Schemes. (AM-104)
- Topological Types of Algebraic Stacks
- An arithmetic count of the lines on a smooth cubic surface
- Groupes de Chow-Witt
- Algebraic Cobordism
- An algebraic approach to the topological degree of a smooth map
- Weil's Conjecture for Function Fields
- Triangulated Categories of Mixed Motives
- Motivic Homotopy Theory and Refined Enumerative Geometry
- MOTIVIC EULER CHARACTERISTICS AND WITT-VALUED CHARACTERISTIC CLASSES
- 𝔸1-contractibility of affine modifications
- Abundance of Real Lines on Real Projective Hypersurfaces
- A1 contractibility of the Koras–Russell threefold
- Homotopical algebraic geometry. II. Geometric stacks and applications
- The real section conjecture and Smith's fixed-point theorem for pro-spaces
- Homotopy Obstructions to Rational Points
- Higher Topos Theory (AM-170)
- \(\mathbb{A}^1\)-homotopy theory of schemes
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Homotopy theory and arithmetic geometry -- motivic and Diophantine aspects: an introduction