Algebraic groups | Algebraic number theory

Tamagawa number

In mathematics, the Tamagawa number of a semisimple algebraic group defined over a global field k is the measure of , where is the adele ring of k. Tamagawa numbers were introduced by Tamagawa, and named after him by Weil. Tsuneo Tamagawa's observation was that, starting from an invariant differential form ω on G, defined over k, the measure involved was well-defined: while ω could be replaced by cω with c a non-zero element of , the product formula for valuations in k is reflected by the independence from c of the measure of the quotient, for the product measure constructed from ω on each effective factor. The computation of Tamagawa numbers for semisimple groups contains important parts of classical quadratic form theory. (Wikipedia).

Video thumbnail

Tokyo 4K - Driving Downtown - Tokyos Times Square

Morning drive from Shibuya (Tokyo Version of New York City's Times Square), to Central Tokyo, to Tokyo Bay neighborhoods by the waterfront. Starting Point: https://goo.gl/maps/16qG57EeHwjTzbR87. Tokyo, Japan’s busy capital, mixes the ultramodern and the traditional, from neon-lit skyscra

From playlist Location by City - Tokyo - J Utah

Video thumbnail

合気道 - 柔らかな護身術 Aikido self-defense techniques

合気道の柔らかな護身術 白川竜次 師範 - 合気会6段 Shirakawa Ryuji shihan - aikikai 6th dan 受け:丸山拓也 Maruyama Takuya , 片山靖和 Katayama Sena Facebook :https://www.facebook.com/aikido.shirakawa Instagram:https://www.instagram.com/ryujishirakawa/ 思わず憧れる!カッコ良くて美しい合気道 https://youtu.be/IwzyRB5hpVQ 白川竜次先生について https:

From playlist Aikido

Video thumbnail

Conversion Arcs and 2,916,485,648,612,232,232,816 (MegaFavNumbers)

I'm sorry. The MegaFavNumbers playlist: https://www.youtube.com/playlist?list=PLar4u0v66vIodqt3KSZPsYyuULD5meoAo

From playlist MegaFavNumbers

Video thumbnail

Tokyo 4K - Skyscraper District - Morning Drive - Shinjuku

Thursday early morning drive through Shinjuku, home of the largest concentration of skyscrapers in Tokyo. Happy holidays everyone! Shinjuku is home to Tokyo's largest concentration of skyscrapers. Several of the tallest buildings in Tokyo are located in this area, including the Tokyo Metr

From playlist Location by City - Tokyo - J Utah

Video thumbnail

Tokyo 4K - Classic Tokyo Neighborhood - Japan

Thursday afternoon drive around the traditional Asakusa neighborhood, known for its rickshaws, rich traditional streets, and historic Japanese temples. The Tokyo Skytree overlooks this neighborhood and can be seen throughout the video. This video is from my visit later last year. One of

From playlist Location by City - Tokyo - J Utah

Video thumbnail

Tamagawa Numbers of Linear Algebraic Groups over (...) - Rosengarten - Workshop 2 - CEB T2 2019

Zev Rosengarten (Hebrew University of Jerusalem) / 26.06.2019 Tamagawa Numbers of Linear Algebraic Groups over Function Fields In 1981, Sansuc obtained a formula for Tamagawa numbers of reductive groups over number fields, modulo some then unknown results on the arithmetic of simply con

From playlist 2019 - T2 - Reinventing rational points

Video thumbnail

Jacob Lurie: 1/5 Tamagawa numbers in the function field case [2019]

Slides for this talk: http://swc-alpha.math.arizona.edu/video/2019/2019LurieLecture1Slides.pdf Lecture notes: http://swc.math.arizona.edu/aws/2019/2019LurieNotes.pdf Let G be a semisimple algebraic group defined over the field Q of rational numbers and let G(Q) denote the group of ration

From playlist Number Theory

Video thumbnail

Recent developments in non-commutative Iwasawa theory I - David Burns

David Burns March 25, 2011 For more videos, visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Tokyo 4K HDR - Driving Downtown - Tokyo Towers

Afternoon drive from Tokyo Tower (Japan's red Eiffel Tower) to the Tokyo Skytree in central Tokyo. One more new location coming soon. And another trip fast approaching. Hope you enjoy the video! Starting Point: https://goo.gl/maps/LU9WsbHJ7Jv9jgFC8. Tokyo, Japan’s busy capital, mixes the

From playlist Location by City - Tokyo - J Utah

Video thumbnail

Dennis Gaitsgory - Tamagawa Numbers and Nonabelian Poincare Duality, II [2013]

Dennis Gaitsgory Wednesday, August 28 4:30PM Tamagawa Numbers and Nonabelian Poincare Duality, II Gelfand Centennial Conference: A View of 21st Century Mathematics MIT, Room 34-101, August 28 - September 2, 2013 Abstract: This will be a continuation of Jacob Lurie’s talk. Let X be an al

From playlist Number Theory

Video thumbnail

Jeffrey Achter, Equidistribution counts abelian varieties

VaNTAGe Seminar, February 22, 2022 License: CC-BY-NC-SA Links to some of the papers mentioned in this talk are listed below. Sutherland: https://arxiv.org/abs/1604.01256 Gekeler: https://academic.oup.com/imrn/article/2003/37/1999/863196 Job Rauch: https://www.universiteitleiden.nl/binar

From playlist Curves and abelian varieties over finite fields

Video thumbnail

囲碁★九路盤対局 -- TAS/lesson in 4:50 (+English captions)

ファミコン 囲碁★九路盤対局 (Igo Kyuu-Roban Taikyoku) 4分50秒 (レベル10) 2007年 9月20日 1回企及 http://tasvideos.org/1704S.html What is Go? Look here> https://bisqwit.iki.fi/jutut/go2.html

From playlist My TASes

Video thumbnail

Dennis Gaitsgory - The Tamagawa number formula over function fields

Séminaire Paris Pékin Tokyo / Mercredi 17 novembre 2015 Let G be a semi-simple and simply connected group and X an algebraic curve. We consider Bun_G(X), the moduli space of G-bundles on X. In their celebrated paper, Atiyah and Bott gave a formula for the cohomology of Bun_G, namely H^*(B

From playlist Conférences Paris Pékin Tokyo

Video thumbnail

Jacob Lurie - Tamagawa Numbers and Nonabelian Poincare Duality, I [2013]

Jacob Lurie Wednesday, August 28 3:10PM Tamagawa Numbers and Nonabelian Poincare Duality, I Gelfand Centennial Conference: A View of 21st Century Mathematics MIT, Room 34-101, August 28 - September 2, 2013 Abstract: Let q and q0 be positive definite integral quadratic forms. We say that

From playlist Number Theory

Video thumbnail

1,010,010,101,000,011 - #MegaFavNumbers

This is my submission to the #megafavnumbers project. My number is 1010010101000011, which is prime in bases 2, 3, 4, 5, 6 and 10. I've open-sourced my code: https://bitbucket.org/Bip901/multibase-primes Clarification: by "ignoring 1" I mean ignoring base 1, since this number cannot be fo

From playlist MegaFavNumbers

Video thumbnail

Special Values of Zeta Functions (Lecture 2) by Matthias Flach

PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla

From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)

Related pages

Dimension of an algebraic variety | Haar measure | Quadratic form | Algebraic group | Differential form | Classical group | Mathematics | Global field | Adele ring | Weil's conjecture on Tamagawa numbers | Algebraic function field | Adelic algebraic group