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 Compositio MathematicaJournal Prestige (SJR): 3.139 Citation Impact (citeScore): 1Number of Followers: 0      Subscription journal ISSN (Print) 0010-437X - ISSN (Online) 1570-5846 Published by Cambridge University Press  [387 journals]
• A Witt Nadel vanishing theorem for threefolds
• Authors: Yusuke Nakamura; Hiromu Tanaka
Pages: 435 - 475
Abstract: In this paper, we establish a vanishing theorem of Nadel type for the Witt multiplier ideals on threefolds over perfect fields of characteristic larger than five. As an application, if a projective normal threefold over $\mathbb{F}_{q}$ is not klt and its canonical divisor is anti-ample, then the number of the rational points on the klt-locus is divisible by $q$ .
PubDate: 2020-03-01T00:00:00.000Z
DOI: 10.1112/S0010437X1900770X
Issue No: Vol. 156, No. 3 (2020)

• ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$\operatorname{Sym}^{2}\mathbb{P}(V)$ ++++++++++++ ++++++++ ++++&rft.title=Compositio+Mathematica&rft.issn=0010-437X&rft.date=2020&rft.volume=156&rft.spage=476&rft.epage=525&rft.aulast=Rennemo&rft.aufirst=Jørgen&rft.au=Jørgen+Vold+Rennemo&rft_id=info:doi/10.1112/S0010437X19007772">The homological projective dual of $\operatorname{Sym}^{2}\mathbb{P}(V)$
• Authors: Jørgen Vold Rennemo
Pages: 476 - 525
Abstract: We study the derived category of a complete intersection $X$ of bilinear divisors in the orbifold $\operatorname{Sym}^{2}\mathbb{P}(V)$ . Our results are in the spirit of Kuznetsov’s theory of homological projective duality, and we describe a homological projective duality relation between $\operatorname{Sym}^{2}\mathbb{P}(V)$ and a category of modules over a sheaf of Clifford algebras on $\mathbb{P}(\operatorname{Sym}^{2}V^{\vee })$ . The proof follows a recently developed strategy combining variation of geometric invariant theory (VGIT) stability and categories of global matrix factorisations. We begin by translating $D^{b}(X)$ into a derived category of factorisations on a Landau–Ginzburg (LG) model, and then apply VGIT to obtain a birational LG model. Finally, we interpret the derived factorisation category of the new LG model as a Clifford module category. In some cases we can compute this Clifford module category as the derived category of a variety. As a corollary we get a new proof of a result of Hosono and Takagi, which says that a certain pair of non-birational Calabi–Yau 3-folds have equivalent derived categories.
PubDate: 2020-03-01T00:00:00.000Z
DOI: 10.1112/S0010437X19007772
Issue No: Vol. 156, No. 3 (2020)

• ++++++++ ++++++++ ++++++++++++ ++++++++++++++++$K(\unicode[STIX]{x1D70B},1)$ ++++++++++++ ++++++++ ++++-problem+for+restrictions+of+complex+reflection+arrangements&rft.title=Compositio+Mathematica&rft.issn=0010-437X&rft.date=2020&rft.volume=156&rft.spage=526&rft.epage=532&rft.aulast=Amend&rft.aufirst=Nils&rft.au=Nils+Amend&rft.au=Pierre+Deligne,+Gerhard+Röhrle&rft_id=info:doi/10.1112/S0010437X19007796">On the $K(\unicode[STIX]{x1D70B},1)$ -problem for restrictions of complex
reflection arrangements
• Authors: Nils Amend; Pierre Deligne, Gerhard Röhrle
Pages: 526 - 532
Abstract: Let $W\subset \operatorname{GL}(V)$ be a complex reflection group and $\mathscr{A}(W)$ the set of the mirrors of the complex reflections in  $W$ . It is known that the complement $X(\mathscr{A}(W))$ of the reflection arrangement $\mathscr{A}(W)$ is a $K(\unicode[STIX]{x1D70B},1)$ space. For $Y$ an intersection of hyperplanes in $\mathscr{A}(W)$ , let $X(\mathscr{A}(W)^{Y})$ be the complement in $Y$ of the hyperplanes in $\mathscr{A}(W)$ not containing
PubDate: 2020-03-01T00:00:00.000Z
DOI: 10.1112/S0010437X19007796
Issue No: Vol. 156, No. 3 (2020)

• Matching of orbital integrals (transfer) and Roche Hecke algebra
isomorphisms
• Authors: Bertrand Lemaire; Manish Mishra
Pages: 533 - 603
Abstract: Let $F$ be a non-Archimedean local field, $G$ a connected reductive group defined and split over $F$ , and $T$ a maximal $F$ -split torus in $G$ . Let $\unicode[STIX]{x1D712}_{0}$ be a depth-zero character of the maximal compact subgroup $T$ of $T(F)$ . This gives by inflation a character $\unicode[STIX]{x1D70C}$ of an Iwahori subgroup $\unicode[STIX]{x2110}\subset T$ of
PubDate: 2020-03-01T00:00:00.000Z
DOI: 10.1112/S0010437X19007838
Issue No: Vol. 156, No. 3 (2020)

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