000			03307nam a22004095a 4500
001			204-160630
003			CH-001817-3
005			20170613140836.0
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008			160630e20160725sz fot ||| 0|eng d
020			_a9783037196571
024	7	0	_a10.4171/157 _2doi
040			_ach0018173
072		7	_aPBV _2bicssc
084			_a05-xx _a11-xx _a13-xx _a14-xx _2msc
245	1	0	_aAbsolute Arithmetic and $\mathbb F_1$-Geometry _h[electronic resource] / _cKoen Thas
260	3		_aZuerich, Switzerland : _bEuropean Mathematical Society Publishing House, _c2016
264		1	_aZuerich, Switzerland : _bEuropean Mathematical Society Publishing House, _c2016
300			_a1 online resource (397 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
505	0	0	_tThe Weyl functor. Introduction to Absolute Arithmetic / _rKoen Thas -- _tBelian categories / _rAnton Deitmar -- _tThe combinatorial-motivic nature of $\mathbb F_1$-schemes / _rKoen Thas -- _tA blueprinted view on $\mathbb F_1$-geometry / _rOliver Lorscheid -- _tAbsolute geometry and the Habiro topology / _rLieven Le Bruyn -- _tWitt vectors, semirings, and total positivity / _rJames Borger -- _tModuli operad over $\mathbb F_1$ / _rYuri I. Manin, Matilde Marcolli -- _tA taste of Weil theory in characteristic one / _rKoen Thas.
506	1		_aRestricted to subscribers: _uhttp://www.ems-ph.org/ebooks.php
520			_aIt 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 experts, and besides elaborating on known results, brand new results, open problems and conjectures are also met along the way. The diversity of the contents, together with the mystery surrounding the field with one element, should attract any mathematician, regardless of speciality.
650	0	7	_aCombinatorics & graph theory _2bicssc
650	0	7	_aCombinatorics _2msc
650	0	7	_aNumber theory _2msc
650	0	7	_aCommutative rings and algebras _2msc
650	0	7	_aAlgebraic geometry _2msc
700	1		_aThas, Koen, _eeditor.
856	4	0	_uhttps://doi.org/10.4171/157
856	4	2	_3cover image _uhttp://www.ems-ph.org/img/books/thas_mini_2016.jpg
942			_2EBK13872 _cEBK
999			_c50496 _d50496