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Chromatic homotopy theory is asymptotically algebraic. (arXiv:1711.00844v2 [math.AT] UPDATED)
来源于:arXiv
Inspired by the Ax--Kochen isomorphism theorem, we develop a notion of
categorical ultraproducts to capture the generic behavior of an infinite
collection of mathematical objects. We employ this theory to give an asymptotic
solution to the approximation problem in chromatic homotopy theory. More
precisely, we show that the ultraproduct of the $E(n,p)$-local categories over
any non-prinicipal ultrafilter on the set of prime numbers is equivalent to the
ultraproduct of certain algebraic categories introduced by Franke. This shows
that chromatic homotopy theory at a fixed height is asymptotically algebraic. 查看全文>>