Algebraic geometry and number theory : Summer School, Galatasaray University, Istanbul, 2014 /
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| Meeting name: | Algebraic Geometry and Number Theory (Summer School) (2014 : Istanbul, Turkey) |
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| Imprint: | Cham, Switzerland : Birkhäuser, 2017. |
| Description: | 1 online resource |
| Language: | English |
| Series: | Progress in mathematics ; volume 321 Progress in mathematics (Boston, Mass.) ; v. 321. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11273657 |
Table of 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 plane; 4. 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 hypersurface; 3. 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 class; 6.3. 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 theorem; 2.3. 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