# Questions tagged [adams-operations]

For questions about Adams operations which are cohomology operations for K theory.

8
questions

**12**

votes

**2**answers

507 views

### Are the real and complex Adams operations compatible under the inclusions $U(n) \rightarrow SO(2n)$?

Does the following diagram commute?
$$
\require{AMScd}
\begin{CD}
BU @>{\psi^k}>> BU \\
@VVV @VVV \\
BO @>{\psi^k}>> BO
\end{CD}
$$
Evidence for: $rc = 2$, it works for $BU(1) \...

**8**

votes

**1**answer

485 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^...

**6**

votes

**0**answers

198 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 ...

**3**

votes

**0**answers

100 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 ...

**10**

votes

**1**answer

459 views

### How to write K-theory Conner-Floyd Chern classes in terms of Adams operations?

From Adams, we know that the algebra of (unstable, degree-zero) cohomology operations $K^0(BU)$ can be written as formal infinite linear combinations of canonical generators
$$\mu_n := \sum_{i=0}^{n}...

**10**

votes

**3**answers

1k 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 ...

**7**

votes

**1**answer

834 views

### Is the Burnside ring a lambda-ring? + conjecture in Knutson p. 113

Warning: I'll be using the "pre-$\lambda$-ring" and "$\lambda$-ring" nomenclature, as opposed to the "$\lambda$-ring" and "special $\lambda$-ring" one (although I just used the latter a few days ago ...

**7**

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\...