A Deligne-Riemann-Roch isomorphism
[Un isomorphisme de Deligne-Riemann-Roch]
Thèses d'Orsay, no. 752 (2008) , 162 p.
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Eriksson, Dennis. A Deligne-Riemann-Roch isomorphism. Thèses d'Orsay, no. 752 (2008), 162 p. http://numdam.org/item/BJHTUP11_2008__0752__P0_0/

Sommaire

Part I p. 1
1. Brauer-Manin obstruction for zero-cycles on curvesp. 3
1.1 Brauer-Manin obstructionp. 3
1.2 A Short Proof of S. Saito’s Theoremp. 7
1.3 Brauer-Manin obstruction and Generic Periodsp. 8
1.4 Alternative Description of the Periodp. 10
1.5 Appendix - Suslin homology, h0p. 12
Part II p. 17
2. Some preliminariesp. 19
2.1 The virtual categoryp. 19
2.2 Algebraic definitionp. 20
2.3 Additional descriptionsp. 22
3. Virtual categories associated to algebraic stacksp. 33
3.1 Various categoriesp. 33
3.2 A splitting principlep. 39
3.3 Adams and λ-operations on the virtual categoryp. 40
3.4 Deformation to the normal conep. 43
4. Rigidity and operations on virtual categoriesp. 47
5. A functorial excess formulap. 61
5.1 A rough excess-isomorphismp. 62
5.2 Excess for projective bundle-morphisms, uniquenessp. 67
5.3 Excess for closed immersions, uniquenessp. 68
5.4 Excess for closed immersions, rougher excess and existencep. 71
5.5 General excess isomorphismp. 80
6. Applications to functorialityp. 85
6.1 Explicit construction of characteristic classesp. 85
6.2 An explicit functorial Lefschetz formula for cyclic diagonal actionsp. 88
6.3 An Adams-Deligne-Riemann-Roch formulap. 98
6.4 Application to Adams-Riemann-Roch transformationsp. 106
6.5 Mumford’s isomorphism and comparison with Deligne’s isomorphismp. 108
6.6 A Deligne-Riemann-Roch formula for the Determinant of the cohomologyp. 114
6.7 A conjecture of Köck for the determinant of the cohomologyp. 115
Appendix p. 119
A. A 1-homotopy theory of schemesp. 121
B. Localization of Picard categories and the case of quotients of split reductive groupsp. 131
C. Algebraic stacksp. 133

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