Suite spectrale du coniveau ett-structure homotopique

Abstract

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Derived equivalent threefolds, algebraic representatives, and the coniveau filtration

“…It is then apparent that the action of v(E) induces the isomorphisms in (1•1). Assuming that K is perfect, the isomorphisms in (1•2) follow readily from the functoriality of the coniveau filtration with respect to the action of correspondences [4,9]. for definitions.…”

On perverse homotopy $t$-structures, coniveau spectral sequences, cycle modules, and relative Gersten weight structures

“…I We can assume that X is reduced (see Theorem 1.4.1( 9)). Now let us apply a more or less standard method for constructing coniveau spectral sequences (see §3 of [Deg13]; in §1 of [CHK97] a closely related argument is described; cf. also §2 of [Deg12]).…”

“…Applying H * to this tower yields an exact couple with [Deg13] or Exercise 2 in §IV.2 of [GeM03]). We denote this couple by EC(X, x !…”

“…2. In §3 of [Deg13] two closely related methods for constructing coniveau spectral sequences were described; one may say that they correspond to "complementary" Postnikov towers. Above we have considered the exact couple corresponding to the method (very much) similar to the one used in [Bon10b] and [Bon13], whereas in §1 of [CHK97] the "complementary" exact couple was considered.…”

“…Above we have considered the exact couple corresponding to the method (very much) similar to the one used in [Bon10b] and [Bon13], whereas in §1 of [CHK97] the "complementary" exact couple was considered. Yet the couples mentioned yield canonically isomorphic spectral sequences (see §3 of [Deg13]); hence the method of calculation of the E 1 -terms of the spectral sequence in §1.2 of [Bon10b] can be applied to 'our' exact couple also. Besides, it is actually not difficult at all to use the "complementary" exact couples in all the arguments above.…”