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Algebraic geometry and number theory : Summer School, Galatasaray University, Istanbul, 2014

Author: Hussein Mourtada; Celal Cem Sarıoğlu; Christophe Soulé; Ayberk Zeytin
Publisher: Cham, Switzerland : Birkhäuser, 2017.
Series: Progress in mathematics (Boston, Mass.), v. 321.
Edition/Format:   eBook : Document : Conference publication : EnglishView all editions and formats
Summary:
This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate  Read more...
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Genre/Form: Electronic books
Conference papers and proceedings
Congresses
Additional Physical Format: (OCoLC)959033553
Material Type: Conference publication, Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Hussein Mourtada; Celal Cem Sarıoğlu; Christophe Soulé; Ayberk Zeytin
ISBN: 9783319477794 331947779X
OCLC Number: 986538838
Description: 1 online resource.
Contents: Preface; List of Participants; p-adic Variation in Arithmetic Geometry: A Survey; 1. Introduction; 2. Kummer congruences; 3. Iwasawa's theory of cyclotomic fields; 4. Iwasawa theory of elliptic curves (and other geometric objects); 4.1. The case K = Q and ran = 1; 4.2. p-adic Birch and Swinnerton-Dyer conjecture and the case ran = 0; 4.2.1. The p-adic L-function; 5. Deformations of Galois representations and Iwasawa theory; 5.1. Deformations of Galois representations; Acknowledgement; References; The Birational Geometry of Moduli Spaces; 1. Introduction; 2. Birational geometry 3. The Hilbert scheme of points on the plane4. Other moduli spaces; 4.1. The moduli space of curves; 4.2. The Kontsevich moduli space; 4.3. Other moduli spaces; Acknowledgement; References; On the Geometry of Hypersurfaces of Low Degrees in the Projective Space; Introduction; 1. Projective spaces and Grassmannians; 1.1. Projective spaces; 1.2. The Euler sequence; 1.3. Grassmannians; 1.4. Linear spaces contained in a subscheme of P(V ); 1.5. Schubert calculus; 2. Projective lines contained in a hypersurface; 2.1. The scheme of lines contained in a hypersurface 2.2. Projective lines contained in a cubic hypersurface3. Cubic surfaces; 3.1. The plane blown up at six points; 3.2. Rationality; 3.3. Picard groups; 4. Unirationality; 4.1. Unirationality; 5. Cubic threefolds; 5.1. Jacobians; 5.1.1. The Picard group; 5.1.2. Intermediate Jacobians; 5.1.3. The Albanese variety; 5.1.4. Principally polarized abelian varieties; 5.2. The Clemens-Griffiths method; 5.3. Abel-Jacobi maps; 5.3.1. For curves; 5.3.2. The Albanese map; 5.3.3. For cubic threefolds; 5.4. Conic bundles and Prym varieties; 6. Cubic fourfolds; 6.1. The fourfold F(X) 6.2. Varieties with vanishing first Chern class6.3. The Hilbert square of a smooth variety; 6.4. Pfaffian cubics; Acknowledgement; References; The Riemann-Roch Theorem in Arakelov Geometry; 1. Some geometry of numbers; 1.1. Class groups; 1.2. Hermitian line bundles and finiteness of the class number; 1.3. Hermitian vector bundles; 1.4. The Riemann-Roch formula in dimension 1: geometric and arithmetic versions; 1.5. Minkowski's convex body theorem and finiteness of the class number; 2. The Grothendieck-Riemann-Roch theorem; 2.1. The Hirzebruch-Riemann-Roch theorem 2.2. The Grothendieck-Riemann-Roch theorem2.3. The curvature formula; 3. Arithmetic Chow groups and characteristic classes; 3.1. Chow groups; 3.2. Arithmetic Chow groups; 4. The arithmetic Riemann-Roch theorem; 4.1. Characteristic classes in arithmetic Chow groups; 4.2. The arithmetic Todd class of the tangent complex; 4.3. Statement of the arithmetic Riemann-Roch theorem ; 4.4. The exotic R-genus; 4.5. The arithmetic Riemann-Roch theorem; 5. Some applications of the arithmetic Riemann-Roch theorem; 5.1. Heights and the arithmetic Hilbert-Samuel theorem
Series Title: Progress in mathematics (Boston, Mass.), v. 321.
Responsibility: Hussein Mourtada, Celal Cem Sarığlu, Christophe Soulé, Ayberk Zeytin, editors.

Abstract:

This lecture notes volume presents significant contributions from the "Algebraic Geometry and Number Theory" Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014.It addresses  Read more...

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