Igor Rostislavovich Shafarevich and his mathematical heritage

DOI10.1134/S0081543819060014zbMath1440.01025OpenAlexW3013734457MaRDI QIDQ2185498

Viktor S. Kulikov, A. N. Parshin, Sergey O. Gorchinskiy, Vladimir L. Popov

Publication date: 4 June 2020

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543819060014

Mathematics Subject Classification ID

Biographies, obituaries, personalia, bibliographies (01A70) History of number theory (11-03) History of algebraic geometry (14-03) History of group theory (20-03)

Cites Work

• Mapping class group and a global Torelli theorem for hyperkähler manifolds
• Every K 3 surface is Kähler
• Group presentation, p-adic analytic groups and lattices in \(SL_ 2({\mathbb{C}})\)
• Abelian and nonabelian mathematics
• Covering spaces of 3-orbifolds
• Simple Lie algebras of small characteristic. VI: Completion of the classification
• Surfaces of type K3 over fields of finite characteristic
• Finiteness theorems for abelian varieties over number fields.
• On degeneration of K3 surfaces
• There are no abelian varieties over \(\mathbb Z\).
• Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication
• Classification of restricted simple Lie algebras
• Applications of the Kaehler-Einstein-Calabi-Yau metric to moduli of K3 surfaces
• Siegel's theorem in the compact case
• The arithmetic of \(K3\) surfaces
• Modular correspondences, heights and isogenies of Abelian varieties
• Nonsimplicity of the group of unimodular automorphisms of the affine plane
• Finiteness theorem for isogenies of abelian varieties over function fields of finite characteristic
• Equivalences of derived categories and \(K3\) surfaces
• Shafarevich maps and plurigenera of algebraic varieties
• Families of reducible algebraic varieties
• Elliptic curves with large rank over function fields
• Calculating and drawing Belyi pairs
• Factor groups of groups of automorphisms of hyperbolic forms with respect to subgroups generated by 2-reflections. Algebro-geometric applications
• On the holomorphic convexity of reductive linear coverings of a projective complex algebraic manifold
• Linear Shafarevich conjecture
• On the Shafarevich conjecture for surfaces of general type over function fields
• Mordells Vermutung über rationale Punkte auf algebraischen Kurven und Funktionenkörper
• A complete determination of the complex quadratic fields of class-number one
• Imaginäre quadratische Zahlkörper mit der Klassenzahl Eins
• Lectures on minimal models and birational transformations of two dimensional schemes
• La conjecture de Weil pour les surfaces K3
• Extensions with given points of ramification.
• Cohomology of abelian varieties over function fields
• Konstruktion algebraischer Zahlkörper mit beliebiger Gruppe von Primzahlpotenzordnung. I
• Diophantine analysis and modular forms
• DEGENERATION OF SEMISIMPLE ALGEBRAS
• On the problem of the 10th discriminant
• On 𝑝-extensions
• A general reciprocity law
• On the construction of fields with a given Galois group of order 𝑙^{𝑎}
• On the problem of imbedding fields
• Construction of fields of algebraic numbers with given solvable Galois group
• Principal Homogeneous Spaces Over Abelian Varieties
• Igor' Rostislavovich Shafarevich (on his sixtieth birthday)
• ON THE APPLICATION OF RAMIFIED COVERINGS IN THE THEORY OF DIOPHANTINE EQUATIONS
• SOLUTION OF THE RESTRICTED BURNSIDE PROBLEM FOR GROUPS OF ODD EXPONENT
• New lower bounds on subgroup growth and homology growth
• Problems of growth and rationality in algebra and topology
• On the situation of nodes of plane curves
• HONDA SYSTEMS OF GROUP SCHEMES OF PERIODp
• GALOIS MODULI OF PERIOD $p$ GROUP SCHEMES OVER A RING OF WITT VECTORS
• SUPERSINGULARK3 SURFACES OVER FIELDS OF CHARACTERISTIC 2
• VECTOR FIELDS ON ELLIPTIC SURFACES
• FANO 3-FOLDS. II
• ON GALOIS EXTENSIONS OF A MAXIMAL CYCLOTOMIC FIELD
• HOLOMORPHIC TENSORS AND VECTOR BUNDLES ON PROJECTIVE VARIETIES
• EXPLICIT FORM OF THE LAW OF RECIPROCITY
• ON THE DEGENERATION OF K3 SURFACES OVER FIELDS OF FINITE CHARACTERISTIC
• ON SOME INFINITE-DIMENSIONAL GROUPS. II
• Dualité sur un corps local à corps résiduel algébriquement clos
• A SOLUTION OF THE RESTRICTED BURNSIDE PROBLEM FOR 2-GROUPS
• Lectures on the Arithmetic Riemann-Roch Theorem. (AM-127)
• PERIODS OF PARABOLIC FORMS AND $ p$-ADIC HECKE SERIES
• Supersingular $K3$ surfaces
• On the Torelli problem for kählerian $K-3$ surfaces
• NON-ARCHIMEDEAN INTEGRATION AND JACQUET-LANGLANDSp-ADICL-FUNCTIONS
• CLASSIFICATION OF SURFACES OF CLASS VII₀WITHb₂= 0
• INTERSECTION THEORY OF DIVISORS ON AN ARITHMETIC SURFACE
• Calabi's conjecture and some new results in algebraic geometry
• On the ricci curvature of a compact kähler manifold and the complex monge-ampére equation, I
• INSEPARABLE MORPHISMS OF ALGEBRAIC SURFACES
• ON QUASI-LOCAL “CLASS FIELDS” OF ELLIPTIC CURVES. I
• FANO 3-FOLDS. I
• DEGENERATIONS OFK3 SURFACES AND ENRIQUES SURFACES
• QUASI-ELLIPTIC SURFACES OF TYPE K3
• The classification of the simple modular Lie algebras: VI. Solving the final case
• Some families of Abelian surfaces
• The tame and the wild automorphisms of polynomial rings in three variables
• Finiteness theorems for K3 surfaces and abelian varieties of CM type
• THE INFLUENCE OF HEIGHT ON DEGENERATIONS OF ALGEBRAIC SURFACES OF TYPE K3
• On uniformity conjectures for abelian varieties and K3 surfaces
• The imbedding problem for local fields
• The Burnside problem
• Principal homogeneous spaces defined over a function field
• On class field towers
• Linear forms in the logarithms of algebraic numbers
• Rational points of algebraic curves over function fields
• Irreducible representations of a simple three-dimensional lie algebra over a field of finite characteristic
• A criterion for projectivity of complete algebraic abstract varieties
• ALGEBRAIC CURVES OVER FUNCTION FIELDS. I
• On a theorem on infinite dimensionality of an associative algebra
• INFINITE PERIODIC GROUPS. I
• The second obstruction for the imbedding problem of algebraic number fields
• FOUNDATIONS OF ALGEBRAIC GEOMETRY
• Classification of vector bundles over an algebraic curve of arbitrary genus
• On the classification of 𝑛-dimensional vector-bundles over an algebraic curve of arbitrary genus
• GRADED LIE ALGEBRAS OF FINITE CHARACTERISTIC
• On nil-algebras and finitely approximable 𝑝-groups
• Galois theory of transcendental extensions and uniformization
• THREE-DIMENSIONAL QUARTICS AND COUNTEREXAMPLES TO THE LÜROTH PROBLEM
• FAMILIES OF ALGEBRAIC CURVES WITH FIXED DEGENERACIES
• A TORELLI THEOREM FOR ALGEBRAIC SURFACES OF TYPEK3
• THE TATE MODULE FOR ALGEBRAIC NUMBER FIELDS
• Topological rings
• Existenz und Mannigfaltigkeit abelscher Algebren mit vorgegebener Galoisgruppe über einem Teilkörper des Grundkörpers. I
• On Algebraic Groups and Homogeneous Spaces
• Local flat duality of abelian varieties
• On the Chern numbers of surfaces of general type
• Local flat duality of abelian varieties
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Igor Rostislavovich Shafarevich and his mathematical heritage