By Kai Behrend, Barbara Fantechi (auth.), Yuri Tschinkel, Yuri Zarhin (eds.)

ISBN-10: 0817647449

ISBN-13: 9780817647445

*Algebra, mathematics, and Geometry: In Honor of Yu. I. Manin* includes invited expository and examine articles on new advancements bobbing up from Manin’s extraordinary contributions to arithmetic.

Contributors within the first quantity include:

okay. Behrend, V.G. Berkovich, J.-B. Bost, P. Bressler, D. Calaque, J.F. Carlson, A. Chambert-Loir, E. Colombo, A. Connes, C. Consani, A. Da˛browski, C. Deninger, I.V. Dolgachev, S.K. Donaldson, T. Ekedahl, A.-S. Elsenhans, B. Enriquez, P. Etingof, B. Fantechi, V.V. Fock, E.M. Friedlander, B. van Geemen, G. van der Geer, E. Getzler, A.B. Goncharov, V.A. Iskovskikh, J. Jahnel, M. Kapranov, E. Looijenga, M. Marcolli, B. Tsygan, E. Vasserot, M. Wodzicki.

**Read Online or Download Algebra, Arithmetic, and Geometry: Volume I: In Honor of Yu. I. Manin PDF**

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**Additional info for Algebra, Arithmetic, and Geometry: Volume I: In Honor of Yu. I. Manin**

**Example text**

A quasi-isomorphism of diﬀerential Gerstenhaber algebras is a morphism of diﬀerential Gerstenhaber algebras that induces an isomorphism of Gerstenhaber algebras on cohomology. 17. Let A be a Gerstenhaber algebra. A sheaf of graded OS modules L with an action of A making L a graded A-module is called a Batalin–Vilkovisky module over A if it is endowed with a C-linear map d : L → L of degree +1 satisfying (i) [d, d] = d2 = 0; (ii) For all X, Y ∈ A and every ω ∈ L we have d(X ∧ Y ω) + (−1)X+Y X ∧ Y dω + (−1)X [X, Y ] ω = (−1)X X d(Y ω) + (−1)XY +Y Y d(X ω) .

12. There are canonical quasi-isomorphisms of diﬀerential Gerstenhaber algebras (M × L) S ×S C −→ L S M and (M × L) S ×S C −→ M In particular, the derived intersections L quasi-isomorphic. S S L . M and M S L are canonically Proof. Passing to étale neighborhoods of L in S and M in S will not change anything about either derived intersection L S M or M S L , so we may assume, without loss of generality, that (i) L is embedded (not just immersed) in S (and the same for M in S ), (ii) L admits a global Euler section t with respect to E on S (and M has the Euler section s in E on S ).

Providence, RI, (1997), 313–318. [195] Semisimple Frobenius (super)manifolds and quantum cohomology of P r (with S. A. Merkulov). Topological Methods in Nonlinear Analysis, 9:1, (1997), 107–161 (Ladyzhenskaya’s Festschrift). [196] Vatican, Fall 1996. Russian: In: Priroda, 8, (1997), 61–66. xxx List of Publications [197] Gauge Field Theory and Complex Geometry, Second Edition (with Appendix by S. Merkulov). Springer Verlag, (1997), xii + 346 pp. [198] Linear Algebra and Geometry (with A. I. Kostrikin), Paperback Edition.

### Algebra, Arithmetic, and Geometry: Volume I: In Honor of Yu. I. Manin by Kai Behrend, Barbara Fantechi (auth.), Yuri Tschinkel, Yuri Zarhin (eds.)

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