Derived -adic categories for algebraic stacks

By K. Behrend. 2003

87 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/77551b23f0032de051923c4ece05f7bcee6f2fe6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Yves Laszlo
2. Jacob Lurie
3. D. Gaitsgory
4. Tomoyuki Abe
5. Martin Olsson
6. B. Noohi
7. Bumsig Kim
8. Carlos Simpson

In Geometry and Topology

1. D. Gaitsgory
2. Carlos Simpson
3. Yves Laszlo
4. Martin Olsson
5. Tomoyuki Abe
6. V. Drinfeld
7. B. Noohi
8. Jacob Lurie

In Mathematical Physics

1. D. Gaitsgory
2. Yves Laszlo
3. Tomoyuki Abe
4. Carlos Simpson
5. Martin Olsson
6. V. Drinfeld
7. B. Noohi
8. Jacob Lurie

Citations in the corpus

• The six operations for sheaves on Artin stacks I: Finite coefficients (2005, background): “It follows that for any F ∈ D(Y) there is a distinguished triangle RH0X (F)→ F→ Rj∗jF→ RH0X (F)[1].”
• FUNDAMENTAL GROUPS OF ALGEBRAIC STACKS (2002, methodology): “cation FUNDAMENTAL GROUPS OF ALGEBRAIC STACKS 25 by monotonous gerbes. We then use this stratification to prove a stronger version of Theorem 6.2. We will need the following lemma, due to Kai Behrend ([1], Section 5), in the proof of our Stratification Theorem (Section 11). Lemma 11.1. Let G → X be a ”
• Higher and derived stacks: a global overview (2009, unknown): “ satisfying some finiteness conditions. These results are out of the scope of the present overview, and the reader will find the details in the forthcoming work [To-Va-Ve]. I would also like to mention [Be] and [La-Ol] where the l-adic formalism has been studied for Artin 1-stacks, and [To3] for a par”
• Langlands correspondence for isocrystals and the existence of crystalline companions for curves (2013, result): “of the equality are finite sums, since we are dealing with c-admissible stacks, contrary to the case of more general algebraic stacks. This prevent us from struggling with the convergence issues as in [Beh], which makes it much easier to formulate and prove. Proof. Since we can prove similarly to [La”
• Weil's Conjecture for Function Fields (2019, background): “However, we will first need to address a more basic question: how is the ring H(BunG(X); Z`) defined? Theories of of `-adic sheaves on Artin stacks have been developed by a number of authors (see, for example, [7] and [32]).”
• Enhanced six operations and base change theorem for higher Artin stacks (2012, unknown): “Derived categories in étale cohomology on Artin stacks and Grothendieck’s six operations between such categories have been developed by many authors including [40] (for Deligne–Mumford stacks), [25], [5], [31] and [24].”