scholarly journals Generic base change, Artin’s comparison theorem, and the decomposition theorem for complex Artin stacks

2016 ◽  
Vol 26 (3) ◽  
pp. 513-555
Author(s):  
Shenghao Sun
Keyword(s):  
Comparison Theorem ◽  
Decomposition Theorem ◽  
Base Change ◽  
Artin Stacks

scholarly journals Functorial destackification of tame stacks with abelian stabilisers

2017 ◽  
Vol 153 (6) ◽  
pp. 1257-1315 ◽  
Author(s):  
Daniel Bergh
Keyword(s):  
Base Change ◽  
Arbitrary Field ◽  
General Base ◽  
Quotient Singularities ◽  
Artin Stacks ◽  
Construction Works

We give an algorithm for removing stackiness from smooth, tame Artin stacks with abelian stabilisers by repeatedly applying stacky blow-ups. The construction works over a general base and is functorial with respect to base change and compositions with gerbes and smooth, stabiliser-preserving maps. As applications, we indicate how the result can be used for destackifying general Deligne–Mumford stacks in characteristic$0$, and to obtain a weak factorisation theorem for such stacks. Over an arbitrary field, the method can be used to obtain a functorial algorithm for desingularising varieties with simplicial toric quotient singularities, without assuming the presence of a toroidal structure.

scholarly journals Iwasawa Theory of Elliptic Modular Forms Over Imaginary Quadratic Fields at Non-ordinary Primes

2019 ◽  
Author(s):  
Kâzım Büyükboduk ◽  
Antonio Lei
Keyword(s):  
Modular Form ◽  
Modular Forms ◽  
Quadratic Field ◽  
Euler System ◽  
Base Change ◽  
Iwasawa Theory ◽  
Imaginary Quadratic Field ◽  
Selmer Groups ◽  
Imaginary Quadratic Fields ◽  
Elliptic Modular Form

AbstractThis article is a continuation of our previous work [7] on the Iwasawa theory of an elliptic modular form over an imaginary quadratic field $K$, where the modular form in question was assumed to be ordinary at a fixed odd prime $p$. We formulate integral Iwasawa main conjectures at non-ordinary primes $p$ for suitable twists of the base change of a newform $f$ to an imaginary quadratic field $K$ where $p$ splits, over the cyclotomic ${\mathbb{Z}}_p$-extension, the anticyclotomic ${\mathbb{Z}}_p$-extensions (in both the definite and the indefinite cases) as well as the ${\mathbb{Z}}_p^2$-extension of $K$. In order to do so, we define Kobayashi–Sprung-style signed Coleman maps, which we use to introduce doubly signed Selmer groups. In the same spirit, we construct signed (integral) Beilinson–Flach elements (out of the collection of unbounded Beilinson–Flach elements of Loeffler–Zerbes), which we use to define doubly signed $p$-adic $L$-functions. The main conjecture then relates these two sets of objects. Furthermore, we show that the integral Beilinson–Flach elements form a locally restricted Euler system, which in turn allow us to deduce (under certain technical assumptions) one inclusion in each one of the four main conjectures we formulate here (which may be turned into equalities in favorable circumstances).

Developing a Genetic System in Deinococcus radiodurans for Analyzing Mutations

Genetics ◽  
2004 ◽  
Vol 166 (2) ◽  
pp. 661-668
Author(s):  
Mandy Kim ◽  
Erika Wolff ◽  
Tiffany Huang ◽  
Lilit Garibyan ◽  
Ashlee M Earl ◽  
...  
Keyword(s):  
Dna Sequences ◽  
Deinococcus Radiodurans ◽  
Genetic System ◽  
Base Change ◽  
Base Substitution ◽  
Wild Type ◽  
Base Pairs ◽  
E Coli ◽  
Radiation Induced ◽  
Induced Mutagenesis

Abstract We have applied a genetic system for analyzing mutations in Escherichia coli to Deinococcus radiodurans, an extremeophile with an astonishingly high resistance to UV- and ionizing-radiation-induced mutagenesis. Taking advantage of the conservation of the β-subunit of RNA polymerase among most prokaryotes, we derived again in D. radiodurans the rpoB/Rif r system that we developed in E. coli to monitor base substitutions, defining 33 base change substitutions at 22 different base pairs. We sequenced >250 mutations leading to Rif r in D. radiodurans derived spontaneously in wild-type and uvrD (mismatch-repair-deficient) backgrounds and after treatment with N-methyl-N′-nitro-N-nitrosoguanidine (NTG) and 5-azacytidine (5AZ). The specificities of NTG and 5AZ in D. radiodurans are the same as those found for E. coli and other organisms. There are prominent base substitution hotspots in rpoB in both D. radiodurans and E. coli. In several cases these are at different points in each organism, even though the DNA sequences surrounding the hotspots and their corresponding sites are very similar in both D. radiodurans and E. coli. In one case the hotspots occur at the same site in both organisms.

scholarly journals Elliptic Fibrations and Kodaira Dimensions of Schreieder’s Varieties

2021 ◽  
Author(s):  
Alice Garbagnati
Keyword(s):  
K3 Surfaces ◽  
Base Change ◽  
Kodaira Dimension ◽  
Elliptic Surface ◽  
Minimal Resolution ◽  
Elliptic Fibrations ◽  
Smooth Model ◽  
Birational Model ◽  
Hodge Numbers ◽  
Rational Elliptic Surface

Abstract We discuss the birational geometry and the Kodaira dimension of certain varieties previously constructed by Schreieder, proving that in any dimension they admit an elliptic fibration and they are not of general type. The $l$-dimensional variety $Y_{(n)}^{(l)}$, which is the quotient of the product of a certain curve $C_{(n)}$ by itself $l$ times by a group $G\simeq \left ({\mathbb{Z}}/n{\mathbb{Z}}\right )^{l-1}$ of automorphisms, was constructed by Schreieder to obtain varieties with prescribed Hodge numbers. If $n=3^c$ Schreieder constructed an explicit smooth birational model of it, and Flapan proved that the Kodaira dimension of this smooth model is 1, if $c>1$; if $l=2$ it is a modular elliptic surface; if $l=3$ it admits a fibration in K3 surfaces. In this paper we generalize these results: without any assumption on $n$ and $l$ we prove that $Y_{(n)}^{(l)}$ admits many elliptic fibrations and its Kodaira dimension is at most 1. Moreover, if $l=2$, its minimal resolution is a modular elliptic surface, obtained by a base change of order $n$ on a specific extremal rational elliptic surface; if $l\geq 3$ it has a birational model that admits a fibration in K3 surfaces and a fibration in $(l-1)$-dimensional varieties of Kodaira dimension at most 0.

scholarly journals Polynomial identities related to special Schubert varieties

2021 ◽  
Author(s):  
Francesca Cioffi ◽  
Davide Franco ◽  
Carmine Sessa
Keyword(s):  
Arbitrary Number ◽  
Schubert Variety ◽  
Decomposition Theorem ◽  
Point Of View ◽  
Explicit Description ◽  
Intersection Cohomology ◽  
Schubert Varieties ◽  
Polynomial Identities ◽  
Poincaré Polynomial

AbstractLet $$\mathcal S$$ S be a single condition Schubert variety with an arbitrary number of strata. Recently, an explicit description of the summands involved in the decomposition theorem applied to such a variety has been obtained in a paper of the second author. Starting from this result, we provide an explicit description of the Poincaré polynomial of the intersection cohomology of $$\mathcal S$$ S by means of the Poincaré polynomials of its strata, obtaining interesting polynomial identities relating Poincaré polynomials of several Grassmannians, both by a local and by a global point of view. We also present a symbolic study of a particular case of these identities.

scholarly journals The resolution property via Azumaya algebras

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Siddharth Mathur
Keyword(s):  
Azumaya Algebras ◽  
Algebraic Space ◽  
Local Methods ◽  
Artin Stacks ◽  
Resolution Property

Abstract Using formal-local methods, we prove that a separated and normal tame Artin surface has the resolution property. By proving that normal tame Artin stacks can be rigidified, we ultimately reduce our analysis to establishing the existence of Azumaya algebras. Our construction passes through the case of tame Artin gerbes, tame Artin curves, and algebraic space surfaces, each of which we establish independently.

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