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2 votes
1 answer
306 views

Serre functors and global dimensions

Let $k$ be a field. Let $\mathcal{C}$ be an abelian category (over $k$). We say that $\mathcal{C}$ has a finite global dimension if there exists integer $n > 0$ such that $$ \operatorname{Ext}^i(M,...
YkMz's user avatar
  • 889
12 votes
0 answers
688 views

Kontsevich's derived noncommutative geometry and Rosenberg's noncommutative 'spaces'

It appears to me (though I may be wrong) that the common opinion is that the main difference between derived noncommutative geometry and Rosenberg's noncommutative 'spaces' is that Rosenberg's version ...
Doelt_k's user avatar
  • 439
16 votes
0 answers
591 views

Lifting DG-categories to characteristic zero

The question of lifting (smooth projective) varieties from an algebraically closed field $k$ of characteristic $p$ to characteristic zero (i.e., to the Witt vectors $W(k)$) is a classical one. It's ...
Akhil Mathew's user avatar
  • 25.6k
6 votes
1 answer
2k views

Hochschild and cyclic homology of smooth varieties

Many of the standard sources which discuss the Hochschild Kostant Rosenberg theorem and cyclic homology for smooth varieties such as Loday and Weibel's paper "The Hodge Filtration and Cyclic Homology" ...
Daniel Pomerleano's user avatar