Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.

Authors:BENSON; DAVE, IYENGAR, SRIKANTH B., KRAUSE, HENNING, PEVTSOVA, JULIA Pages: 1 - 24 Abstract: A duality theorem for the singularity category of a finite dimensional Gorenstein algebra is proved. It complements a duality on the category of perfect complexes, discovered by Happel. One of its consequences is an analogue of Serre duality, and the existence of Auslander–Reiten triangles for the -local and -torsion subcategories of the derived category, for each homogeneous prime ideal arising from the action of a commutative ring via Hochschild cohomology. PubDate: 2020-03-11 DOI: 10.1017/nmj.2020.2

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Authors:QUINLAN-GALLEGO; EAMON Pages: 25 - 34 Abstract: Following the work of Mustaţă and Bitoun, we recently developed a notion of Bernstein–Sato roots for arbitrary ideals, which is a prime characteristic analogue for the roots of the Bernstein–Sato polynomial. Here, we prove that for monomial ideals the roots of the Bernstein–Sato polynomial (over ) agree with the Bernstein–Sato roots of the mod reductions of the ideal for large enough. We regard this as evidence that the characteristic- notion of Bernstein–Sato root is reasonable. PubDate: 2020-03-20 DOI: 10.1017/nmj.2020.3

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Authors:DORFMEISTER; JOSEF F., WANG, PENG Pages: 35 - 59 Abstract: A Willmore surface has a natural harmonic oriented conformal Gauss map , which maps each point to its oriented mean curvature 2-sphere at . An easy observation shows that all conformal Gauss maps of Willmore surfaces satisfy a restricted nilpotency condition, which will be called “strongly conformally harmonic.” The goal of this paper is to characterize those strongly conformally harmonic maps from a Riemann surface to , which are the conformal Gauss maps of some Willmore surface in It turns out that generically, the condition of being strongly conformally harmonic suffices to be associated with a Willmore surface. The exceptional case will also be discussed. PubDate: 2020-04-27 DOI: 10.1017/nmj.2020.6

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Authors:MANION; ANDREW, MARENGON, MARCO, WILLIS, MICHAEL Pages: 60 - 118 Abstract: We give a generators-and-relations description of differential graded algebras recently introduced by Ozsváth and Szabó for the computation of knot Floer homology. We also compute the homology of these algebras and determine when they are formal. PubDate: 2020-04-17 DOI: 10.1017/nmj.2020.7

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Authors:MOSS; GILBERT Pages: 119 - 135 Abstract: Let be a -adic field and choose an algebraic closure of , with different from . We define “nilpotent lifts” of irreducible generic -representations of , which take coefficients in Artin local -algebras. We show that an irreducible generic -modular representation of is uniquely determined by its collection of Rankin–Selberg gamma factors PubDate: 2020-05-12 DOI: 10.1017/nmj.2020.8

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Authors:IKEDA; AKISHI Pages: 136 - 157 Abstract: In the pioneering work by Dimitrov–Haiden–Katzarkov–Kontsevich, they introduced various categorical analogies from the classical theory of dynamical systems. In particular, they defined the entropy of an endofunctor on a triangulated category with a split generator. In the connection between the categorical theory and the classical theory, a stability condition on a triangulated category plays the role of a measured foliation so that one can measure the “volume” of objects, called the mass, via the stability condition. The aim of this paper is to establish fundamental properties of the growth rate of mass of objects under the mapping by the endofunctor and to clarify the relationship between it and the entropy. We also show that they coincide under a certain condition. PubDate: 2020-06-04 DOI: 10.1017/nmj.2020.9

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Authors:SAORÍN; MANUEL, ZIMMERMANN, ALEXANDER Pages: 158 - 167 Abstract: In previous work, based on the work of Zwara and Yoshino, we defined and studied degenerations of objects in triangulated categories analogous to the degeneration of modules. In triangulated categories , it is surprising that the zero object may degenerate. We show that the triangulated subcategory of generated by the objects that are degenerations of zero coincides with the triangulated subcategory of consisting of the objects with a vanishing image in the Grothendieck group of . PubDate: 2020-06-08 DOI: 10.1017/nmj.2020.10

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Authors:STEIN; OLIVER Pages: 168 - 203 Abstract: We prove a functional equation for a vector valued real analytic Eisenstein series transforming with the Weil representation of on . By relating such an Eisenstein series with a real analytic Jacobi Eisenstein series of degree , a functional equation for such an Eisenstein series is proved. Employing a doubling method for Jacobi forms of higher degree established by Arakawa, we transfer the aforementioned functional equation to a zeta function defined by the eigenvalues of a Jacobi eigenform. Finally, we obtain the analytic continuation and a functional equation of the standard -function attached to a Jacobi eigenform, which was already proved by Murase, however in a different way. PubDate: 2020-07-21 DOI: 10.1017/nmj.2020.11

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Authors:FEDELE; FRANCESCA Pages: 204 - 231 Abstract: Let be a field, and let be a -linear, Hom-finite triangulated category with split idempotents. In this paper, we show that under suitable circumstances, the Grothendieck group of , denoted by , can be expressed as a quotient of the split Grothendieck group of a higher cluster tilting subcategory of . The results we prove are higher versions of results on Grothendieck groups of triangulated categories by Xiao and Zhu and by Palu. Assume that is an integer; has a Serre functor and an -cluster tilting subcategory such that is locally bounded. Then, for every indecomposable PubDate: 2020-06-11 DOI: 10.1017/nmj.2020.12

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Authors:WESTAWAY; MATTHEW Pages: 232 - 255 Abstract: Steinberg’s tensor product theorem shows that for semisimple algebraic groups, the study of irreducible representations of higher Frobenius kernels reduces to the study of irreducible representations of the first Frobenius kernel. In the preceding paper in this series, deforming the distribution algebra of a higher Frobenius kernel yielded a family of deformations called higher reduced enveloping algebras. In this paper, we prove that the Steinberg decomposition can be similarly deformed, allowing us to reduce representation theoretic questions about these algebras to questions about reduced enveloping algebras. We use this to derive structural results about modules over these algebras. Separately, we also show that many of the results in the preceding paper hold without an assumption of reductivity. PubDate: 2020-06-02 DOI: 10.1017/nmj.2020.13

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Authors:FUJINO; OSAMU Pages: 256 - 282 Abstract: We establish the minimal model theory for -factorial log surfaces and log canonical surfaces in Fujiki’s class . PubDate: 2020-06-05 DOI: 10.1017/nmj.2020.14

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Authors:KAHN; BRUNO, MIYAZAKI, HIROYASU Pages: 283 - 313 Abstract: We study relationships between the Nisnevich topology on smooth schemes and certain Grothendieck topologies on proper and not necessarily proper modulus pairs, which were introduced in previous papers. Our results play an important role in the theory of sheaves with transfers on proper modulus pairs. PubDate: 2020-07-13 DOI: 10.1017/nmj.2020.15