Suslin’s moving lemma with modulus

Abstract

The moving lemma of Suslin states that a cycle on X × A n meeting all faces properly can be moved so that it becomes equidimensional over A n . This leads to an isomorphism of motivic Borel-Moore homology and higher Chow groups.In this short paper we formulate and prove a variant of this. It leads to an isomorphism of Suslin homology with modulus and higher Chow groups with modulus, in an appropriate pro setting. Recently the context has been extended to cycles with modulus by Binda-Kerz-Saito [KS, BS] and Kahn-Saito-Yamazaki [KSY]. The reader finds the definitions below. There is an obvious injection (r ≥ 0)for each pair (X, Y ) consisting of a finite type k-scheme X and an effective Cartier divisor Y on it. We usually write X := X \ Y .

Investigation of (S)-(−)-Acidomycin: A Selective Antimycobacterial Natural Product That Inhibits Biotin Synthase

“…After 16 h, the reaction mixture was concentrated in vacuo, and re-dissolved in Et 2 O (250 mL), washed with H 2 O (2 × 150 mL), dried (MgSO 4 ) and concentrated in vacuo to yield the title compound (26 g, 99 %) as a colorless oil which was used in the next step without purification: R f = 0.31 (1:1 EtOAchexanes); 1 H, 13 C NMR and MS match previously reported spectra. 87…”

“…The aqueous layer was extracted with CH 2 Cl 2 (2 × 100 mL), and combined extracts were washed with 5 % (w/v) aqueous potassium bisulfate (150 mL), 5 % (w/v) aqueous sodium thiosulfate (150 mL), saturated aqueous NaCl (150 mL), dried (MgSO 4 ), and concentrated in vacuo to give an orange oil which was purified by high vacuum fractional distillation (75-85 °C under 0.9 torr) to give the title compound (1.8 g, 91 %) as a colorless oil: R f = 0.47 (3:7 EtOAc-hexanes); 1 H, 13 C NMR and MS match previously reported spectra. 87…”