ISBN: 3037191570

[SR: 850691], Hardcover, [EAN: 9783037191576], European Mathematical Society, European Mathematical Society, Book, [PU: European Mathematical Society], European Mathematical Society, It h… Mehr…

[SR: 850691], Hardcover, [EAN: 9783037191576], European Mathematical Society, European Mathematical Society, Book, [PU: European Mathematical Society], European Mathematical Society, It has been known for some time that geometries over finite fields, their automorphism groups and certain counting formulae involving these geometries have interesting guises when one lets the size of the field go to 1. On the other hand, the nonexistent field with one element, F1, presents itself as a ghost candidate for an absolute basis in Algebraic Geometry to perform the Deninger-Manin program, which aims at solving the classical Riemann Hypothesis. This book, which is the first of its kind in the F1-world, covers several areas in F1-theory and is divided into four main parts: Combinatorial Theory, Homological Algebra, Algebraic Geometry and Absolute Arithmetic. Topics treated include the combinatorial theory and geometry behind F1, categorical foundations, the blend of different scheme theories over F1 which are presently available, motives and zeta functions, the Habiro topology, Witt vectors and total positivity, moduli operads, and at the end, even some arithmetic. Each chapter is carefully written by an expert. In addition to elaborating on known results, the authors introduce brand-new results, open problems and conjectures. The diversity of the contents, together with the mystery surrounding the field with one element, should attract any mathematician, regardless of speciality., 13907, Combinatorics, 226698, Pure Mathematics, 13884, Mathematics, 75, Science & Math, 1000, Subjects, 283155, Books, 468218, Mathematics, 491542, Algebra & Trigonometry, 491544, Calculus, 491546, Geometry, 491548, Statistics, 468216, Science & Mathematics, 465600, New, Used & Rental Textbooks, 2349030011, Specialty Boutique, 283155, Books<

ISBN: 9783037191576

It has been known for some time that geometries over finite fields, their automorphism groups and certain counting formulae involving these geometries have interesting guises when one let… Mehr…

It has been known for some time that geometries over finite fields, their automorphism groups and certain counting formulae involving these geometries have interesting guises when one lets the size of the field go to 1. On the other hand, the nonexistent field with one element, $\mathbb{F}_1$, presents itself as a ghost candidate for an absolute basis in Algebraic Geometry to perform the Deninger-Manin program, which aims at solving the classical Riemann Hypothesis. This book, which is the first of its kind in the $\mathbb{F}_1$-world, covers several areas in $\mathbb{F}_1$-theory and is divided into four main parts: Combinatorial Theory, Homological Algebra, Algebraic Geometry and Absolute Arithmetic. Topics treated include the combinatorial theory and geometry behind $\mathbb{F}_1$, categorical foundations, the blend of different scheme theories over $\mathbb{F}_1$ which are presently available, motives and zeta functions, the Habiro topology, Witt vectors and total positivity, moduli operads, and at the end, even some arithmetic. Each chapter is carefully written by an expert. In addition to elaborating on known results, the authors introduce brand-new results, open problems and conjectures. The diversity of the contents, together with the mystery surrounding the field with one element, should attract any mathematician, regardless of speciality. Trade Books>Hardcover>Science>Mathematics>Mathematics, European Mathematical Society Core >2<

ISBN: 9783037191576

Absolute Arithmetic and F1-Geometry Absolute-Arithmetic-and-F1-Geometry~~Koen-Thas Science>Mathematics>Mathematics Hardcover, European Mathematical Society

2016, ISBN: 9783037191576

Gebundene Ausgabe

[ED: 1], Hardcover, Buch, [PU: European Mathematical Society Publishing House]

2016, ISBN: 9783037191576

Gebundene Ausgabe

Buch, Hardcover, [PU: EMS Press], [ED: 1], EMS Press, 2016