LEADER 00983cam0-22003251i-450- 001 990004528060403321 005 20091019140750.0 035 $a000452806 035 $aFED01000452806 035 $a(Aleph)000452806FED01 035 $a000452806 100 $a19990604d1952----km-y0itay50------ba 101 0 $agrc 102 $aNL 105 $ay-------001yy 200 1 $aOpera ascetica$fGregorii Nysseni$gediderunt Wernerus Jaeger, Johannes P. Cavarnos, Virginia Woods Callahan 210 $aLeiden$cBrill$d1952 215 $aVI, 416 p.$d25 cm 225 1 $aGregorii Nysseni Opera$v8 700 1$aGregorius Nyssenus,$csanto$f$0181219 702 1$aCallahan Woods,$bVirginia 702 1$aCavarnos,$bJohn Peter 702 1$aJaeger,$bWerner Wilhelm 801 0$aIT$bUNINA$gRICA$2UNIMARC 901 $aBK 912 $a990004528060403321 952 $a7-VIIIC2(6)$bBIBL.32742$fFLFBC 959 $aFLFBC 996 $aOpera ascetica$9548362 997 $aUNINA LEADER 03318nam 22004695a 450 001 9910153279503321 005 20160630234501.0 010 $a3-03719-657-2 024 70$a10.4171/157 035 $a(CKB)3340000000002766 035 $a(CH-001817-3)204-160630 035 $a(PPN)194913732 035 $a(EXLCZ)993340000000002766 100 $a20160630j20160725 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAbsolute Arithmetic and $\mathbb F_1$-Geometry$b[electronic resource] /$fKoen Thas 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2016 215 $a1 online resource (397 pages) 311 $a3-03719-157-0 327 $tThe Weyl functor. Introduction to Absolute Arithmetic /$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. 330 $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. 606 $aCombinatorics & graph theory$2bicssc 606 $aCombinatorics$2msc 606 $aNumber theory$2msc 606 $aCommutative rings and algebras$2msc 606 $aAlgebraic geometry$2msc 615 07$aCombinatorics & graph theory 615 07$aCombinatorics 615 07$aNumber theory 615 07$aCommutative rings and algebras 615 07$aAlgebraic geometry 686 $a05-xx$a11-xx$a13-xx$a14-xx$2msc 701 $aThas$b Koen$f1977-$0726617 801 0$bch0018173 906 $aBOOK 912 $a9910153279503321 996 $aAbsolute Arithmetic and$92564511 997 $aUNINA LEADER 04856nam 22007455 450 001 996466663503316 005 20200701010914.0 010 $a3-642-23669-3 024 7 $a10.1007/978-3-642-23669-3 035 $a(CKB)3390000000021680 035 $a(SSID)ssj0000609363 035 $a(PQKBManifestationID)11433923 035 $a(PQKBTitleCode)TC0000609363 035 $a(PQKBWorkID)10625703 035 $a(PQKB)11413119 035 $a(DE-He213)978-3-642-23669-3 035 $a(MiAaPQ)EBC3070395 035 $a(PPN)159084725 035 $a(EXLCZ)993390000000021680 100 $a20120104d2012 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aComplex Monge?Ampère Equations and Geodesics in the Space of Kähler Metrics$b[electronic resource] /$fedited by Vincent Guedj 205 $a1st ed. 2012. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2012. 215 $a1 online resource (VIII, 310 p. 4 illus.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2038 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-642-23668-5 320 $aIncludes bibliographical references. 327 $a1.Introduction -- I. The Local Homogenious Dirichlet Problem.-2. Dirichlet Problem in Domains of Cn -- 3. Geometric Maximality -- II. Stochastic Analysis for the Monge-Ampère Equation -- 4. Probabilistic Approach to Regularity -- III. Monge-Ampère Equations on Compact Manifolds -- 5.The Calabi-Yau Theorem -- IV Geodesics in the Space of Kähler Metrics -- 6. The Riemannian Space of Kähler Metrics -- 7. MA Equations on Manifolds with Boundary -- 8. Bergman Geodesics. 330 $aThe purpose of these lecture notes is to provide an introduction to the theory of complex Monge?Ampère operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Kähler manifolds (with or without boundary). These operators are of central use in several fundamental problems of complex differential geometry (Kähler?Einstein equation, uniqueness of constant scalar curvature metrics), complex analysis and dynamics. The topics covered include, the Dirichlet problem (after Bedford?Taylor), Monge?Ampère foliations and laminated currents, polynomial hulls and Perron envelopes with no analytic structure, a self-contained presentation of Krylov regularity results, a modernized proof of the Calabi?Yau theorem (after Yau and Kolodziej), an introduction to infinite dimensional riemannian geometry, geometric structures on spaces of Kähler metrics (after Mabuchi, Semmes and Donaldson), generalizations of the regularity theory of Caffarelli?Kohn?Nirenberg?Spruck (after Guan, Chen and Blocki) and Bergman approximation of geodesics (after Phong?Sturm and Berndtsson). Each chapter can be read independently and is based on a series of lectures by R. Berman, Z. Blocki, S. Boucksom, F. Delarue, R. Dujardin, B. Kolev and A. Zeriahi, delivered to non-experts. The book is thus addressed to any mathematician with some interest in one of the following fields, complex differential geometry, complex analysis, complex dynamics, fully non-linear PDE's and stochastic analysis. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2038 606 $aFunctions of complex variables 606 $aDifferential geometry 606 $aPartial differential equations 606 $aAlgebraic geometry 606 $aSeveral Complex Variables and Analytic Spaces$3https://scigraph.springernature.com/ontologies/product-market-codes/M12198 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 608 $aAufsatzsammlung. 615 0$aFunctions of complex variables. 615 0$aDifferential geometry. 615 0$aPartial differential equations. 615 0$aAlgebraic geometry. 615 14$aSeveral Complex Variables and Analytic Spaces. 615 24$aDifferential Geometry. 615 24$aPartial Differential Equations. 615 24$aAlgebraic Geometry. 676 $a515/.7242 686 $aSI 850$2rvk 686 $aMAT 146f$2stub 686 $aMAT 322f$2stub 686 $aMAT 354f$2stub 686 $aMAT 537f$2stub 686 $a510$2sdnb 702 $aGuedj$b Vincent$4edt$4http://id.loc.gov/vocabulary/relators/edt 906 $aBOOK 912 $a996466663503316 996 $aComplex Monge?Ampère equations and geodesics in the space of Kähler metrics$91417443 997 $aUNISA