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Coherent sheaves, superconnections, and Riemann-Roch-Grothendieck

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Coherent sheaves, superconnections, and Riemann-Roch-Grothendieck/ by Jean-Michel Bismut, Shu Shen, Zhaoting Wei.
Author:	Bismut, Jean-Michel.
other author:	Shen, Shu.
Published:	Cham :Springer International Publishing : : 2023.,
Description:	x, 184 p. :illustrations, digital ; : 24 cm.;
Contained By:	Springer Nature eBook
Subject:	Grothendieck groups. -
Online resource:	https://doi.org/10.1007/978-3-031-27234-9
ISBN:	9783031272349

Coherent sheaves, superconnections, and Riemann-Roch-Grothendieck
Bismut, Jean-Michel.

Coherent sheaves, superconnections, and Riemann-Roch-Grothendieck[electronic resource] /by Jean-Michel Bismut, Shu Shen, Zhaoting Wei. - Cham :Springer International Publishing :2023. - x, 184 p. :illustrations, digital ;24 cm. - Progress in mathematics,v. 3472296-505X ;. - Progress in mathematics ;v.231..

This monograph addresses two significant related questions in complex geometry: the construction of a Chern character on the Grothendieck group of coherent sheaves of a compact complex manifold with values in its Bott-Chern cohomology, and the proof of a corresponding Riemann-Roch-Grothendieck theorem. One main tool used is the equivalence of categories established by Block between the derived category of bounded complexes with coherent cohomology and the homotopy category of antiholomorphic superconnections. Chern-Weil theoretic techniques are then used to construct forms that represent the Chern character. The main theorem is then established using methods of analysis, by combining local index theory with the hypoelliptic Laplacian. Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck is an important contribution to both the geometric and analytic study of complex manifolds and, as such, it will be a valuable resource for many researchers in geometry, analysis, and mathematical physics.

ISBN: 9783031272349

Standard No.: 10.1007/978-3-031-27234-9doiSubjects--Topical Terms:

1434738
Grothendieck groups.

LC Class. No.: QA613.618

Dewey Class. No.: 516.183

Coherent sheaves, superconnections, and Riemann-Roch-Grothendieck
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245 1 0 $a Coherent sheaves, superconnections, and Riemann-Roch-Grothendieck $h [electronic resource] / $c by Jean-Michel Bismut, Shu Shen, Zhaoting Wei.
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490 1 $a Progress in mathematics, $x 2296-505X ; $v v. 347
520 $a This monograph addresses two significant related questions in complex geometry: the construction of a Chern character on the Grothendieck group of coherent sheaves of a compact complex manifold with values in its Bott-Chern cohomology, and the proof of a corresponding Riemann-Roch-Grothendieck theorem. One main tool used is the equivalence of categories established by Block between the derived category of bounded complexes with coherent cohomology and the homotopy category of antiholomorphic superconnections. Chern-Weil theoretic techniques are then used to construct forms that represent the Chern character. The main theorem is then established using methods of analysis, by combining local index theory with the hypoelliptic Laplacian. Coherent Sheaves, Superconnections, and Riemann-Roch-Grothendieck is an important contribution to both the geometric and analytic study of complex manifolds and, as such, it will be a valuable resource for many researchers in geometry, analysis, and mathematical physics.
650 0 $a Grothendieck groups. $3 1434738
650 0 $a Chern classes. $3 1434739
650 0 $a Complexes. $3 672125
650 1 4 $a Category Theory, Homological Algebra. $3 678397
650 2 4 $a K-Theory. $3 672463
650 2 4 $a Differential Equations. $3 681826
650 2 4 $a Differential Geometry. $3 671118
700 1 $a Shen, Shu. $3 1434736
700 1 $a Wei, Zhaoting. $3 1434737
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830 0 $a Progress in mathematics ; $v v.231. $3 882991
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950 $a Mathematics and Statistics (SpringerNature-11649)