Topological methods of algebraic geometry | Cohomology theories | Homotopical algebra

Motivic cohomology

Motivic cohomology is an invariant of algebraic varieties and of more general schemes. It is a type of cohomology related to motives and includes the Chow ring of algebraic cycles as a special case. Some of the deepest problems in algebraic geometry and number theory are attempts to understand motivic cohomology. (Wikipedia).

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Matthew Morrow - Motivic cohomology of formal schemes in characteristic p

Mardi 29 mars 2016 The logarithmic Hodge-Witt sheaves of Illusie, Milne, Kato, et al. of a smooth variety in characteristic p provide a concrete realisation of its p-adic motivic cohomology, thanks to results of Geisser-Levine and Bloch-Kato-Gabber which link them to algebraic K-theory. I

From playlist Conférences Paris Pékin Tokyo

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Daniel Isaksen - 2/3 Motivic and Equivariant Stable Homotopy Groups

Notes: https://nextcloud.ihes.fr/index.php/s/EyZRRtDq965o6WC I will discuss a program for computing C2-equivariant, ℝ-motivic, ℂ-motivic, and classical stable homotopy groups, emphasizing the connections and relationships between the four homotopical contexts. The Adams spectral sequence

From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

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Federico Binda - Triangulated Categories of Log Motives over a Field

In this talk I will sketch the construction and highlight the main properties of a new motivic category for logarithmic schemes, log smooth over a ground field k (without log structure). This construction is based on a new Grothendieck topology (called the “dividing topology”) and on the p

From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

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Dianel Isaksen - 3/3 Motivic and Equivariant Stable Homotopy Groups

Notes: https://nextcloud.ihes.fr/index.php/s/4N5kk6MNT5DMqfp I will discuss a program for computing C2-equivariant, ℝ-motivic, ℂ-motivic, and classical stable homotopy groups, emphasizing the connections and relationships between the four homotopical contexts. The Adams spectral sequence

From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

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Daniel Isaksen - 1/3 Motivic and Equivariant Stable Homotopy Groups

Notes: https://nextcloud.ihes.fr/index.php/s/F2BoSJ7zgfipRxP I will discuss a program for computing C2-equivariant, ℝ-motivic, ℂ-motivic, and classical stable homotopy groups, emphasizing the connections and relationships between the four homotopical contexts. The Adams spectral sequence

From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

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Dmitry Kaledin - 2/3 Motives from the Non-commutative Point of View

Motives were initially conceived as a way to unify various cohomology theories that appear in algebraic geometry, and these can be roughly divided into two groups: theories of etale type, and theories of cristalline/de Rham type. The obvious unifying feature of all the theories is that the

From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

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Dmitry Kaledin - 3/3 Motives from the Non-commutative Point of View

Motives were initially conceived as a way to unify various cohomology theories that appear in algebraic geometry, and these can be roughly divided into two groups: theories of etale type, and theories of cristalline/de Rham type. The obvious unifying feature of all the theories is that the

From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

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Dmitry Kaledin - 1/3 Motives from the Non-commutative Point of View

Motives were initially conceived as a way to unify various cohomology theories that appear in algebraic geometry, and these can be roughly divided into two groups: theories of etale type, and theories of cristalline/de Rham type. The obvious unifying feature of all the theories is that the

From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

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Motivic cohomology actions and the geometry of eigenvarieties - David Hansen

David Hansen Columbia University October 1, 2015 http://www.math.ias.edu/calendar/event/87325/1443731400/1443735000 Venkatesh has recently proposed a fascinating conjecture relating motivic cohomology with automorphic forms and the cohomology of arithmetic groups. I'll describe this conj

From playlist Joint IAS/PU Number Theory Seminar

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Cohomologies for rigid analytic varieties via motivic homotopy theory by Alberto Vezzani

PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath

From playlist Perfectoid Spaces 2019

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Stable Homotopy without Homotopy - Toni Mikael Annala

IAS/Princeton Arithmetic Geometry Seminar Topic: Stable Homotopy without Homotopy Speaker: Toni Mikael Annala Affiliation: Member, School of Mathematics Date: January 30, 2023 Many cohomology theories in algebraic geometry, such as crystalline and syntomic cohomology, are not homotopy in

From playlist Mathematics

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Automorphic forms and motivic cohomology I - Akshay Venkatesh

Locally Symmetric Spaces Seminar Topic: Automorphic forms and motivic cohomology I Speaker: Akshay Venkatesh Affiliation: Stanford University; Distinguished Visiting Professor, School of Mathematics Date: November 14, 2017 For more videos, please visit http://video.ias.edu

From playlist Mathematics

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Motivic action on coherent cohomology of Hilbert modular varieties - Aleksander Horawa

Joint IAS/Princeton University Number Theory Seminar Topic: Motivic action on coherent cohomology of Hilbert modular varieties Speaker: Aleksander Horawa Affiliation: University of Michigan Date: February 03, 2022 A surprising property of the cohomology of locally symmetric spaces is tha

From playlist Mathematics

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Lie Fu: K-theoretical and motivic hyperKähler resolution conjecture

The lecture was held within the framework of the Hausdorff Trimester Program : Workshop "K-theory in algebraic geometry and number theory"

From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"

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De Rham Cohomology: PART 1- THE IDEA

Credits: Animation: I animated the video myself, using 3Blue1Brown's amazing Python animation library "manim". Link to manim: https://github.com/3b1b/manim Link to 3Blue1Brown: https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw Beyond inspecting the source code myself, this channel

From playlist Cohomology

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On descending cohomology geometrically - Sebastian Casalaina-Martin

Sebastian Casalaina-Martin University of Colorado at Boulder January 20, 2015 In this talk I will present some joint work with Jeff Achter concerning the problem of determining when the cohomology of a smooth projective variety over the rational numbers can be modeled by an abelian variet

From playlist Mathematics

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Automorphic forms and motivic cohomology III - Akshay Venkatesh

Locally Symmetric Spaces Seminar Topic: Automorphic forms and motivic cohomology III Speaker: Akshay Venkatesh Affiliation: Stanford University; Distinguished Visiting Professor, School of Mathematics Date: November 28, 2017 For more videos, please visit http://video.ias.edu

From playlist Mathematics

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Derived de Rham Cohomology - Bhargav Bhatt

Bhargav Bhatt University of Michigan; Member, School of Mathematics September 25, 2012 For more videos, visit http://video.ias.edu

From playlist Mathematics

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Etale motivic cohomology and algebraic cycles - Vasudenvan Srinvas

Vasudevan Srinivas March 9, 2015 Workshop on Chow groups, motives and derived categories More videos on http://video.ias.edu

From playlist Mathematics

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