Algebra, Arithmetic, and Geometry: Volume II: In Honor of Yu. I. Manin

699 Pages·2009·4.33 MB·English

by  Michael Harris (auth.)

Progress in Mathematics
Volume270
SeriesEditors
HymanBass
JosephOesterlé
AlanWeinstein
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Algebra, Arithmetic,
and Geometry
In Honor of Yu. I. Manin
Volume II
Yuri Tschinkel
Yuri Zarhin
Editors
Birkhäuser
Boston (cid:129) Basel (cid:129) Berlin
Editors
YuriTschinkel YuriZarhin
NewYorkUniversity PennsylvaniaStateUniversity
DepartmentofMathematics EberlyCollegeofScience
NewYork,NY10012-1185 DepartmentofMathematics
[email protected] UniversityPark,PA16802
[email protected]
ISBN978-0-8176-4746-9 e-ISBN978-0-8176-4747-6
DOI10.1007/978-0-8176-4747-6
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v

Preface
Yuri Ivanovich Manin has made outstanding contributions to algebra,
algebraic geometry, number theory, algorithmic complexity, noncommutative
geometry and mathematical physics. His numerous achievements include the
proof of the functional analogue of the Mordell Conjecture, the theory of the
Gauss–Manin connection, proof with V. Iskovskikh of the nonrationality of
smooth quartic threefolds, the theory of p-adic automorphic functions, con-
struction of instantons (jointly with V. Drinfeld, M. Atiyah and N. Hitchin),
and the theory of quantum computations.
We hope that the papers in this Festschrift, written in honor of Yu. I.
Manin’s seventieth birthday, will indicate the great respect and admiration
thathisstudents,friendsandcolleaguesthroughouttheworldallhaveforhim.
June 2009
Courant Institute Yuri Tschinkel
Penn State University Yuri Zarhin
vii

Contents
Preface ........................................................ vii
Contents of Volume I .......................................... xi
Potential Automorphy of Odd-Dimensional Symmetric
Powers of Elliptic Curves and Applications
Michael Harris .................................................. 1
Cyclic Homology with Coefficients
D. Kaledin ...................................................... 23
Noncommutative Geometry and Path Integrals
Mikhail Kapranov ................................................ 49
Another Look at the Dwork Family
Nicholas M. Katz ................................................ 89
Graphs, Strings, and Actions
Ralph M. Kaufmann..............................................127
Quotients of Calabi–Yau Varieties
János Kollár and Michael Larsen ..................................179
Notes on Motives in Finite Characteristic
Maxim Kontsevich ...............................................213
PROPped-Up Graph Cohomology
M. Markl and A.A. Voronov.......................................249
Symboles de Manin et valeurs de fonctions L
Loïc Merel ......................................................283
Graph Complexes with Loops and Wheels
S.A. Merkulov ...................................................311
ix