**2**

votes

**0**answers

172 views

### Equivariant Riemann-Roch on DM stacks?

Does an equivariant version of (Toen)-Riemann-Roch theorem hold say over a smooth Deligne-Mumford stack $X$ over the complex numbers?
Any references that state this explicitely?
Are there formulas ...

**7**

votes

**0**answers

118 views

### Riemann-Roch for curves over Dedekind domains and base-change for modular forms

In p-adic properties of modular schemes and modular forms Katz formulates the following base change theorem as Theorem 1.7.1
Let $n\geq 3$ and $\overline{\mathcal{M}}_n$ be the compactified moduli ...

**6**

votes

**2**answers

907 views

### Faltings-Riemann-Roch Theorem

I found the famous Faltings book ``Lectures on arithmetic Riemann-Roch theorem".
In the book, very analytic techniques such as Garding inequality or heat kernel are explained. I have no idea where ...

**7**

votes

**4**answers

647 views

### $\lambda$-ring structure defined for a graded ring in Fulton-Lang's book

Given a commutative ring $A$ with unity, Grothendieck used universal polynomials to define a special $\lambda$-ring structure on $\Lambda(A):=1+t\:A[[t]]$. Suppose $A$ is graded, say ...

**6**

votes

**1**answer

560 views

### Serre duality and Hirzebruch-Riemann-Roch in the non-projective case

Serre duality and the Hirzebruch-Riemann-Roch formula are usually stated for $X$ a smooth projective algebraic variety. Do you know of a reference which proves these results for $X$ smooth and proper?
...