scholarly journals Logarithmic geometry and algebraic stacks

2003 ◽  
Vol 36 (5) ◽  
pp. 747-791 ◽  
Author(s):  
M OLSSON
Keyword(s):  
Algebraic Stacks ◽  
Logarithmic Geometry

scholarly journals The category of toric stacks

2009 ◽  
Vol 145 (03) ◽  
pp. 718-746 ◽  
Author(s):  
Isamu Iwanari
Keyword(s):  
Geometric Characterization ◽  
Free Resolutions ◽  
Algebraic Stacks ◽  
Combinatorial Aspect ◽  
Logarithmic Geometry ◽  
Minimal Free Resolutions

AbstractIn this paper, we show that there is an equivalence between the 2-category of smooth Deligne–Mumford stacks with torus embeddings and actions and the 1-category of stacky fans. To this end, we prove two main results. The first is related to a combinatorial aspect of the 2-category of toric algebraic stacks defined by I. Iwanari [Logarithmic geometry, minimal free resolutions and toric algebraic stacks, Preprint (2007)]; we establish an equivalence between the 2-category of toric algebraic stacks and the 1-category of stacky fans. The second result provides a geometric characterization of toric algebraic stacks. Logarithmic geometry in the sense of Fontaine–Illusie plays a central role in obtaining our results.

Representations of the fundamental group and the torsor of deformations. Global aspects

2017 ◽  
Author(s):  
Ahmed Abbes ◽  
Michel Gros
Keyword(s):  
Fundamental Group ◽  
Koszul Complex ◽  
Finiteness Conditions ◽  
Inverse Systems ◽  
Logarithmic Geometry

This chapter continues the construction and study of the p-adic Simpson correspondence and presents the global aspects of the theory of representations of the fundamental group and the torsor of deformations. After fixing the notation and general conventions, the chapter develops preliminaries and then introduces the results and complements on the notion of locally irreducible schemes. It also fixes the logarithmic geometry setting of the constructions and considers a number of results on the Koszul complex. Finally, it develops the formalism of additive categories up to isogeny and describes the inverse systems of a Faltings ringed topos, with a particular focus on the notion of adic modules and the finiteness conditions adapted to this setting. The chapter rounds up the discussion with sections on Higgs–Tate algebras and Dolbeault modules.

scholarly journals STEENROD OPERATIONS ON THE DE RHAM COHOMOLOGY OF ALGEBRAIC STACKS

2021 ◽  
pp. 1-48
Author(s):  
Federico Scavia
Keyword(s):  
Finite Groups ◽  
Reductive Groups ◽  
Orthogonal Groups ◽  
De Rham Cohomology ◽  
Algebraic Stacks ◽  
Steenrod Operations ◽  
De Rham

Abstract Building upon work of Epstein, May and Drury, we define and investigate the mod p Steenrod operations on the de Rham cohomology of smooth algebraic stacks over a field of characteristic $p>0$ . We then compute the action of the operations on the de Rham cohomology of classifying stacks for finite groups, connected reductive groups for which p is not a torsion prime and (special) orthogonal groups when $p=2$ .

Algebraic stacks

2001 ◽  
Vol 111 (1) ◽  
pp. 1-31 ◽  
Author(s):  
Tomás L Gómez
Keyword(s):  
Algebraic Stacks

The pro-étale topology for algebraic stacks

2020 ◽  
Vol 48 (9) ◽  
pp. 3761-3770
Author(s):  
Chang-Yeon Chough
Keyword(s):  
Algebraic Stacks

scholarly journals Geometricity for derived categories of algebraic stacks

2016 ◽  
Vol 22 (4) ◽  
pp. 2535-2568 ◽  
Author(s):  
Daniel Bergh ◽  
Valery A. Lunts ◽  
Olaf M. Schnürer
Keyword(s):  
Derived Categories ◽  
Algebraic Stacks

scholarly journals Moduli of Bridgeland semistable objects on 3-folds and Donaldson–Thomas invariants

2019 ◽  
Vol 2019 (747) ◽  
pp. 175-219 ◽  
Author(s):  
Dulip Piyaratne ◽  
Yukinobu Toda
Keyword(s):  
Finite Type ◽  
Equivalent Form ◽  
Stability Conditions ◽  
Weak Stability ◽  
Algebraic Stacks ◽  
Moduli Stacks ◽  
Étale Quotients

Abstract In this paper we show that the moduli stacks of Bridgeland semistable objects on smooth projective 3-folds are quasi-proper algebraic stacks of finite type if they satisfy the Bogomolov–Gieseker (BG for short) inequality conjecture proposed by Bayer, Macrì and the second author. The key ingredients are the equivalent form of the BG inequality conjecture and its generalization to arbitrary very weak stability conditions. This result is applied to define Donaldson–Thomas invariants counting Bridgeland semistable objects on smooth projective Calabi–Yau 3-folds satisfying the BG inequality conjecture, for example on étale quotients of abelian 3-folds.

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