Questions tagged [adams-operations]
For questions about Adams operations which are cohomology operations for K theory.
9 questions
14
votes
2
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555
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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) \...
- 141
10
votes
1
answer
575
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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}...
- 2,044
10
votes
3
answers
2k
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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 ...
- 63.1k
10
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1
answer
1k
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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 ...
- 33.8k
9
votes
1
answer
415
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Linear recurrence relation for symmetric powers in the Burnside ring
Let $G$ be a finite group and $B(G)$ be its Burnside ring, i.e. formal sums of isomorphism classes of finite $G$-sets with addition given by disjoint union and multiplication given by Cartesian ...
8
votes
2
answers
1k
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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\...
- 33.8k
8
votes
1
answer
640
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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^...
- 2,871
6
votes
0
answers
220
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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 ...
- 5,901
3
votes
0
answers
127
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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 ...
- 5,901