http://mathoverflow.net/search?q=Riemann-Roch
Soulé, Gillet???
Soule in Asterisque 311: Genres de Todd etc. “The paper starts with a lucid introduction to Arakelov geometry, arithmetic Riemann-Roch, and equivariant RR”
Faltings.
Hirzebruch: Top methods in AG. In folder AG/Various. Covers the Todd genus, and talks about RR.
Notes by Roy Smith in folder AG/Various
Baum, Fulton, MacPherson: Riemann-Roch for singular varieties (1975)
DeLand statement and proof sketch
Chern classes and RR formalism at Concrete Nonsense
Toen preprint: Notes sure la G-theorie… file Toen web unpubl gtdm.pdf. Dsicusses RR formula for stacks, the rational G-theory spectrum of DM stacks over general bases, equivariant K-th.
Toen: Thm de RR pour les champs de DM. File Toen web publ rrchamp.pdf. Discusses K-theory and RR for DM stacks, but also various notions of descent, including basic stuff on simplicial presheaves, homological descent, and etale descent.
RR for stacks, see Toen thesis, under Toen web unpubl folder.
Gillet and Soule: On the number of lattice points etc, has a kind or RR thm, but also an erratum in 2009. http://www.ams.org/mathscinet-getitem?mr=1135244
Kim should know about arithmetic RR theorems.
LNM0210 Eichler: Projective varieties and modular forms. Studies RR with the Dedekind-Weber approach (which allows for singularities) rather than the Weil approach. Applications to varieties of Siegel and Hilbert modular forms, also def and brief intro to these kinds of forms.
Riou on RR theorem via A1-homotopy theory: http://front.math.ucdavis.edu/0907.2710
http://mathoverflow.net/questions/10630/why-todd-classes-appear-in-grothendieck-riemann-roch-formula
http://mathoverflow.net/questions/11746/is-there-grothendieck-riemann-roch-for-abelian-category
arXiv:0907.2710 Algebraic K-theory, A^1-homotopy and Riemann-Roch theorems from arXiv Front: math.AG by Joël Riou. In this article, we show that the combination of the constructions done in SGA 6 and the A^1-homotopy theory naturally leads to results on higher algebraic K-theory. This applies to the operations on algebraic K-theory, Chern characters and Riemann-Roch theorems.
arXiv:1205.0266 The excess formula in functorial form from arXiv Front: math.AG by Dennis Eriksson This article is motivated by the need for better understanding of refined Riemann-Roch theorems and the behavior of the determinant of the cohomology. This poses a certain problem of functoriality and can be understood as that of giving refined constructions of operations in algebraic -theory. In this article this is specialized to mean refining the excess formula, which measures the failure of base change, to the level of Deligne’s virtual category. We give a natural set of properties for such a refinement, and prove that there exists a unique family of excess formulas on this refined level satisfying these properties.
nLab page on Riemann-Roch theorem