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8 votes
1 answer
640 views

Original reference for Adams Riemann-Roch theorem

Let $f\colon Y\to X$ be a proper morphism between smooth quasiprojective $k$-algebraic varieties. Denote by $\psi^j$ the $j$-th Adams operation on the Grothendieck group of vector bundles and $\theta^...
Tintin's user avatar
  • 2,871
6 votes
0 answers
220 views

Adams operation on Q-construction of fields

Let $F$ be a field that we want to compute its rational algebraic $K$-theory using the Quillen's $Q$-construction. Let $QF$ be the $Q$ construction of the category of finite dimensional vector spaces ...
user127776's user avatar
  • 5,901
3 votes
0 answers
127 views

Adams operation on the rational homology

The Adams operation acts on the algebraic $K$-theory of $R$ but the action as far as I know doesn't come from a endo-functor on the category of projective modules over $R$. For the $K_0$ there is an ...
user127776's user avatar
  • 5,901
10 votes
3 answers
2k views

Pullback along Frobenius morphism

Let $X$ be a scheme over a finite field $\mathbb{F}_q$ and let $F : X \to X$ be the absolute Frobenius morphism. If $\mathcal{L}$ is an invertible $\mathcal{O}_X$-module, then there is a natural ...
Martin Brandenburg's user avatar
8 votes
2 answers
1k views

Is every Adams ring morphism a lambda-ring morphism?

A lambda-ring $R$ is called "special" if it satisfies the $\lambda^i\left(xy\right)=...$ and $\lambda^i\left(\lambda^j\left(x\right)\right)=...$ relations, or, equivalently, if the map $\lambda_T:R\to\...
darij grinberg's user avatar