BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Christian Liedtke (https://www.groups.ma.tum.de/algebra/liedtke/) DTSTART:20210202T120000Z DTEND:20210202T140000Z DTSTAMP:20260422T213011Z UID:ShafarevichSeminar/1 DESCRIPTION:Title: Quotient singularities in positive characteristic\nby Chris tian Liedtke (https://www.groups.ma.tum.de/algebra/liedtke/) as part of Sh afarevich seminar\n\n\nAbstract\nWe study isolated quotient singularities by finite group schemes in positive characteristic. We compute invariants\ , study the uniqueness of the quotient presentation\, and compute some\nde formation spaces. A special emphasis is laid on the dichotomy between quot ient singularities by linearly reductive group schemes and by group scheme s that are not linearly reductive. We essentially classify the linearly re ductive ones\, give applications\, and make some conjectures. This is join t work with Gebhard Martin (Bonn) and Yuya Matsumoto (Tokyo).\n LOCATION:https://researchseminars.org/talk/ShafarevichSeminar/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Valery Lunts (Indiana University Bloomington) DTSTART:20210209T120000Z DTEND:20210209T140000Z DTSTAMP:20260422T213011Z UID:ShafarevichSeminar/2 DESCRIPTION:Title: Neron-Severi Lie algebra\, group of autoequivalences of the der ived category\, and monodromy\nby Valery Lunts (Indiana University Blo omington) as part of Shafarevich seminar\n\n\nAbstract\nLet $X$ be a smoot h complex projective manifold\, $G^{eq}(X)\\subset GL(H(X))$ --- the image of the group $Aut(D(X))$ in the group of automorphisms of $H(X)$. First I will explain about the\nrelation of the group $G^{eq}(X)$ and the Neron-S everi Lie algebra. Then I plan to discuss the conjecture of Kontsevich on the relation of the group $G^{eq}(X)$ (if $X$ is CY) with the monodromy gr oup of the mirror symmetric family.\n LOCATION:https://researchseminars.org/talk/ShafarevichSeminar/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuri Prokhorov (Steklov Mathematical Institute of RAS\, NRU HSE) DTSTART:20210216T120000Z DTEND:20210216T140000Z DTSTAMP:20260422T213011Z UID:ShafarevichSeminar/3 DESCRIPTION:Title: Tetragonal conic bundles\nby Yuri Prokhorov (Steklov Mathem atical Institute of RAS\, NRU HSE) as part of Shafarevich seminar\n\nAbstr act: TBA\n LOCATION:https://researchseminars.org/talk/ShafarevichSeminar/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Ivan Panin (St. Petersburg Department of Steklov Mathematical Inst itute of RAS) DTSTART:20210224T120000Z DTEND:20210224T140000Z DTSTAMP:20260422T213011Z UID:ShafarevichSeminar/4 DESCRIPTION:Title: Some results on injectivity and purity in the mixed characteris tic case\nby Ivan Panin (St. Petersburg Department of Steklov Mathemat ical Institute of RAS) as part of Shafarevich seminar\n\n\nAbstract\nLet $ \\mathcal O$ be a discrete valuation ring of mixed\ncharacteristic. For ce rtain class of abelian group presheaves on the\ncategory of $\\mathcal O$- smooth schemes we will discuss injectivity and purity\ntheorems. In partic ular\, we will discuss the Grothendieck-Serre\nconjecture for some classic al groups. We will focus on statements\nand methods. Proofs will be only s ketched.\n LOCATION:https://researchseminars.org/talk/ShafarevichSeminar/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Marc Levine (Duisburg-Essen University) DTSTART:20210302T120000Z DTEND:20210302T140000Z DTSTAMP:20260422T213011Z UID:ShafarevichSeminar/5 DESCRIPTION:Title: Some quadratic conductor formulas\nby Marc Levine (Duisburg -Essen University) as part of Shafarevich seminar\n\n\nAbstract\nA smooth projective variety over a\nfield k defines a dualizable object in the moti vic stable homotopy\nover k\, and thereby an Euler characteristic in the e ndomorphism ring\nof the unit. A theorem of Morel identifies this endomorp hism ring\nwith the Grothendieck-Witt ring of quadratic forms over k and w ith\nA. Raksit\, we have shown that this quadratic Euler characteristic is \ngiven by the intersection form on Hodge cohomology. We use the\ncomputat ion of Hodge cohomology of hypersurfaces via the Jacobian\nring to give an explicit description of the categorical Euler\ncharacteristic of a smooth hypersurface and use this to give\nexamples of a quadratic conductor form ula for certain\ndegenerations. There are mysterious "error terms" that ma kes the\nformula deviate from what one might expect at first glance. These \nerror terms disappear over the complex numbers and also over the\nreal n umbers\, but are in general non-zero.\n LOCATION:https://researchseminars.org/talk/ShafarevichSeminar/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Peternell (Bayreuth University) DTSTART:20210309T120000Z DTEND:20210309T140000Z DTSTAMP:20260422T213011Z UID:ShafarevichSeminar/6 DESCRIPTION:Title: Projective flatness and applications to uniformization\nby Thomas Peternell (Bayreuth University) as part of Shafarevich seminar\n\n\ nAbstract\nI will discuss a Chern class criterion to when a semistable she af on a mildly singular variety is projectively flat and apply this to the uniformization of varieties with nef anticanonical bundles ("singular sem ipositive Ricci").\n LOCATION:https://researchseminars.org/talk/ShafarevichSeminar/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Alexander Efimov (Steklov Mathematical Institute of RAS) DTSTART:20210316T120000Z DTEND:20210316T140000Z DTSTAMP:20260422T213011Z UID:ShafarevichSeminar/7 DESCRIPTION:Title: Nuclear modules over proper DG algebras\nby Alexander Efimo v (Steklov Mathematical Institute of RAS) as part of Shafarevich seminar\n \n\nAbstract\nI will explain a certain construction of a dualizable presen table DG category Nuc(A) of "nuclear modules" over a proper DG algebra A. As a special case this construction gives the category of nuclear modules on an affine formal scheme (more precisely\, its "unbounded" version)\, wh ich was defined recently by Clausen and Scholze. For a smooth and proper D G algebra A the category Nuc(A) is equivalent to the usual category of A-m odules.\n\nI will also explain that this construction is a special case of internal Hom in an appropriate symmetric monoidal category (where the obj ects are dualizable presentable DG categories\, and the morphisms are stro ngly continuous functors).\n LOCATION:https://researchseminars.org/talk/ShafarevichSeminar/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Umberto Zannier (Scuola Normale Superiore\, Pisa) DTSTART:20210323T120000Z DTEND:20210323T140000Z DTSTAMP:20260422T213011Z UID:ShafarevichSeminar/8 DESCRIPTION:Title: Abelian varieties not isogenous to any Jacobian\nby Umberto Zannier (Scuola Normale Superiore\, Pisa) as part of Shafarevich seminar\ n\n\nAbstract\nIt is well known that in dimension $g\\ge 4$ there exist co mplex abelian varieties not isogenous to any Jacobian. A question of Katz and Oort asked whether one can find\nsuch examples over the field of algeb raic numbers. This was answered affirmatively by Oort-Chai under the Andr é-Oort conjecture\, and by Tsimerman unconditionally. They gave examples within Complex Multiplication. In joint work with Masser\, by means of a c ompletely\ndifferent method\, we proved that in a sense the general abelia n variety over $\\overline{\\mathbb Q}$ is indeed not isogenous to any Jac obian. I shall illustrate the basic principles of the proofs.\n LOCATION:https://researchseminars.org/talk/ShafarevichSeminar/8/ END:VEVENT END:VCALENDAR