# A Riemann-Roch-Hirzebruch formula for traces of differential operators

Markus Engeli; Giovanni Felder

Annales scientifiques de l'École Normale Supérieure (2008)

- Volume: 41, Issue: 4, page 623-655
- ISSN: 0012-9593

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topEngeli, Markus, and Felder, Giovanni. "A Riemann-Roch-Hirzebruch formula for traces of differential operators." Annales scientifiques de l'École Normale Supérieure 41.4 (2008): 623-655. <http://eudml.org/doc/272132>.

@article{Engeli2008,

abstract = {Let $D$ be a holomorphic differential operator acting on sections of a holomorphic vector bundle on an $n$-dimensional compact complex manifold. We prove a formula, conjectured by Feigin and Shoikhet, giving the Lefschetz number of $D$ as the integral over the manifold of a differential form. The class of this differential form is obtained via formal differential geometry from the canonical generator of the Hochschild cohomology $HH^\{2n\}(\mathcal \{D\}_n,\mathcal \{D\}_n^*)$ of the algebra of differential operators on a formal neighbourhood of a point. If $D$ is the identity, the formula reduces to the Riemann-Roch-Hirzebruch formula.},

author = {Engeli, Markus, Felder, Giovanni},

journal = {Annales scientifiques de l'École Normale Supérieure},

keywords = {traces of differential operators; Lefschetz formula; Riemann–Roch–Hirzebruch formula},

language = {eng},

number = {4},

pages = {623-655},

publisher = {Société mathématique de France},

title = {A Riemann-Roch-Hirzebruch formula for traces of differential operators},

url = {http://eudml.org/doc/272132},

volume = {41},

year = {2008},

}

TY - JOUR

AU - Engeli, Markus

AU - Felder, Giovanni

TI - A Riemann-Roch-Hirzebruch formula for traces of differential operators

JO - Annales scientifiques de l'École Normale Supérieure

PY - 2008

PB - Société mathématique de France

VL - 41

IS - 4

SP - 623

EP - 655

AB - Let $D$ be a holomorphic differential operator acting on sections of a holomorphic vector bundle on an $n$-dimensional compact complex manifold. We prove a formula, conjectured by Feigin and Shoikhet, giving the Lefschetz number of $D$ as the integral over the manifold of a differential form. The class of this differential form is obtained via formal differential geometry from the canonical generator of the Hochschild cohomology $HH^{2n}(\mathcal {D}_n,\mathcal {D}_n^*)$ of the algebra of differential operators on a formal neighbourhood of a point. If $D$ is the identity, the formula reduces to the Riemann-Roch-Hirzebruch formula.

LA - eng

KW - traces of differential operators; Lefschetz formula; Riemann–Roch–Hirzebruch formula

UR - http://eudml.org/doc/272132

ER -

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