BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ruben Louis (University of Illinos Urbana-Champaign Urbana) DTSTART:20260408T120000Z DTEND:20260408T130000Z DTSTAMP:20260430T090639Z UID:PHK-cohomology-seminar/158 DESCRIPTION:Title: On construction of differential Z-graded varieties (Joint work with A. Hancharuk)\nby Ruben Louis (University of Illinos Urbana -Champaign Urbana) as part of Prague-Hradec Kralove seminar Cohomology in algebra\, geometry\, physics and statistics\n\nLecture held in ZOOM meetin g.\n\nAbstract\nGiven a commutative unital algebra O\, a proper ideal I⊂ O\, and a positively graded differential variety over O/I\, we construct a Z-graded extension whose negative part is an arborescent Koszul–Tate re solution of O/I. This extension is obtained by means of an explicit algori thm that exploits the homotopy retract data of the arborescent Koszul–Ta te resolution\, thereby significantly reducing the number of homological c omputations required in the construction.\n\nWhen the positively graded di fferential variety is defined over O and preserves the ideal I\, the exten sion admits a canonical and explicit description in terms of decorated tre es together with the associated computed data.\n\nAs a by-product\, to eve ry Lie–Rinehart algebra over the coordinate ring of an affine variety W\ , we associate an explicit differential Z-graded variety. Its negative com ponent is the arborescent Koszul–Tate resolution of the coordinate ring ​ of W\, while its positive component is the universal dg-variety of the given Lie–Rinehart algebra.\n\nThese constructions also yield applicati ons to singular foliation theory\, extending results of C. Laurent-Gengoux \, S. Lavau\, and T. Strobl. Explicit examples are provided.\n LOCATION:https://researchseminars.org/talk/PHK-cohomology-seminar/158/ END:VEVENT END:VCALENDAR