000			02870cam a2200385 i 4500
001			on1437991837
003			OCoLC
005			20240806145327.0
008			240611t20242024riua b 000 0 eng d
020			_a1470469626 _q(pbk.)
020			_a9781470469627 _q(pbk.)
035			_a(OCoLC)1437991837
040			_aYDX _beng _erda _cYDX _dYSM _dEAU _dOCLCO _dVGM _dUNBCA _dPAU
100	1		_aAyala, David, _d1982- _eauthor. _1https://id.oclc.org/worldcat/entity/E39PCjt6xjYVPYdTtCq8XHGtBq
245	1	0	_aStratified noncommutative geometry / _cDavid Ayala, Aaron Mazel-Gee, Nick Rozenblyum.
264		1	_aProvidence, RI : _bAmerican Mathematical Society, _c2024.
264		4	_c©2024
300			_av, 260 pages : _billustrations ; _c26 cm.
336			_atext _btxt _2rdacontent
337			_aunmediated _bn _2rdamedia
338			_avolume _bnc _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society, _x0065-9266 ; _vv. 1485
504			_aIncludes bibliographical references (pages 257-260).
520	3		_aWe introduce a theory of stratifications of noncommutative stacks (i.e. presentable stable ∞-categories), and we prove a reconstruction theorem that expresses them in terms of their strata and gluing data. This reconstruction theorem is compatible with symmetric monoidal structures, and with more general operadic structures such as En-monoidal structures. We also provide a suite of fundamental operations for constructing new stratifications from old ones: restriction, pullback, quotient, pushforward, and refinement. Moreover, we establish a dual form of reconstruction; this is closely related to Verdier duality and reflection functors, and gives a categorification of Möbius inversion. Our main application is to equivariant stable homotopy theory: for any compact Lie group G, we give a symmetric monoidal stratification of genuine G-spectra. In the case that G is finite, this expresses genuine G-spectra in terms of their geometric fixedpoints (as homotopy-equivariant spectra) and gluing data therebetween (which are given by proper Tate constructions). We also prove an adelic reconstruction theorem; this applies not just to ordinary schemes but in the more general context of tensor-triangular geometry, where we obtain a symmetric monoidal stratification over the Balmer spectrum. We discuss the particular example of chromatic homotopy theory.
650		0	_aGeometry, Algebraic.
650		0	_aAlgebraic topology.
650		0	_aCategories (Mathematics)
700	1		_aMazel-Gee, Aaron, _eauthor.
700	1		_aRozenblyum, Nick, _d1984- _eauthor. _1https://id.oclc.org/worldcat/entity/E39PCjqCTgHMVBKHbdcfdxhQ4m
830		0	_aMemoirs of the American Mathematical Society ; _vv. 1485.
942			_2ddc _cBK _n0
948			_hNO HOLDINGS IN P5A - 11 OTHER HOLDINGS
999			_c41434 _d41434