All Questions
7 questions with no upvoted or accepted answers
6
votes
0
answers
162
views
$K_0$ of arithmetic surfaces
In his paper "Algebraic K-Theory and classfield theory of arithmetic surfaces", Annals of Mathematics 114 (1981), Spencer Bloch proved the following result: if $A$ is a finitely generated ...
6
votes
0
answers
144
views
$K_0$ an $KH_0$ of a normal crossing variety
Let $k$ be a field (say, algebraically closed to fix the ideas) and let $X$ be a strict (aka simple) normal crossing variety over $k$, so that $X$ is union of regular varieties with intersection that ...
- 61
5
votes
0
answers
415
views
Modern context for hypercohomology spectra
In Thomason's paper Algebraic K-theory and étale cohomology, (Ann. ENS 1985, Numdam link) Thomason develops an elaborate theory of hypercohomology spectra, $\mathbb{H}(X,\mathcal{F})$ for presheafs of ...
- 254
4
votes
0
answers
226
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K-theoretic derivation of Bézout theorem
In the paper "$K$-Theory and Intersection Theory" by Henri Gillet in Handbook of K-theory, 2005 (link behind paywall at Springerlink), the author says:
"When the ground field $k = \mathbb C$, Bézout’...
2
votes
0
answers
416
views
Do we have the following "devissage commutative diagram" in K-theory?
Let $X$ be a non-reduced Noetherian scheme. We define $K^0(X)$ to be the Grothendieck group of the derived category $Perf(X)$ and $K_0(X)$ to be the Grothendieck group of the derived category $D^b_{...
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1
vote
0
answers
206
views
Motivic cohomology commutes with field extension
$\DeclareMathOperator\Cor{Cor}$Let $X$ be a smooth scheme over $k$ and $k \subset F$ a field extension. Let $X_F$ be the field extension of $X$. Then there is a map
$$\varinjlim_{k\subset E \subset F} ...
- 1,168
1
vote
0
answers
94
views
Relative Gersten resolution for a flat projective morphism
I am reading two papers by Daniel Grayson: "Localization for flat modules in algebraic K-theory" and "Algebraic cycles and algebraic K-theory" and I am wondering if any recent advances in K-theory ...
