hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Lang's theorem
In algebraic geometry, Lang's theorem, introduced by Serge Lang, states: if G is a connected smooth algebraic group over a finite field , then, writing  for the Frobenius, the morphism of varieties

is surjective. Note that the kernel of this map (i.e., ) is precisely .

The theorem implies that   
vanishes,  and, consequently, any G-bundle on  is isomorphic to the trivial one. Also, the theorem plays a basic role in the theory of finite groups of Lie type.

It is not necessary that G is affine. Thus, the theorem also applies to abelian varieties (e.g., elliptic curves.) In fact, this application was Lang's initial motivation. If G is affine, the Frobenius  may be replaced by any surjective map with finitely many fixed points (see below for the precise statement.)

The proof (given below) actually goes through for any  that induces a nilpotent operator on the Lie algebra of G.

Torsor (algebraic geometry)
In algebraic geometry, a torsor or a principal bundle is an analogue of a principal bundle in algebraic topology. Because there are few open sets in Zariski topology, it is more common to consider torsors in étale topology or some other flat topologies. The notion also generalizes a Galois extension in abstract algebra. Though other notions of torsors are known in more general context (e.g. over stacks) this article will focus on torsors over schemes, the original setting where torsors have been thought for. The word torsor comes from the French torseur. They are indeed widely discussed, for instance, in Michel Demazure's and Pierre Gabriel's famous book Groupes algébriques, Tome I.
Country rock
Country rock is a music genre that fuses rock and country. It was developed by rock musicians who began to record country-flavored records and country musicians who implemented rock flavor into country records in the late 1960s and early 1970s. These musicians recorded records blending rock with country themes, vocal styles, and additional instrumentation, most characteristically pedal steel guitars. Country rock began in the late 60s with artists like the Nitty Gritty Dirt Band, International Submarine Band, The Flying Burrito Brothers, The Byrds, Bob Dylan, Bob Seger and Poco, reaching its greatest popularity in the 1970s with artists such as Eagles, Grateful Dead, Gram Parsons and New Riders of the Purple Sage. Country rock also influenced artists in other genres, including The Band, the Grateful Dead, Creedence Clearwater Revival, The Rolling Stones, and George Harrison's solo work, as well as playing a part in the development of Southern rock.

Bernie Leadon
Bernard Matthew Leadon III (/ˈlɛdən/ LED-ən; born July 19, 1947) is an American singer, musician, songwriter, and founding member of the Eagles, for which he was inducted into the Rock and Roll Hall of Fame in 1998. Prior to the Eagles, he was a member of four country rock bands: Hearts & Flowers, Dillard & Clark, Linda Ronstadt & the Corvettes and the Flying Burrito Brothers. He is a multi-instrumentalist (guitar, banjo, mandolin, steel guitar, dobro) coming from a bluegrass background. He introduced elements of this music to a mainstream audience during his tenure with the Eagles.

Leadon's solo career since leaving the Eagles has been sporadic, resulting in two albums under his name (the first being a collaborative project with Michael Georgiades) with a gap of 27 years in between. However, Leadon appeared on many other artists' records as a session musician.
Lift Your Spirit
Lift Your Spirit is the third studio album by American musician Aloe Blacc. The album was released on October 25, 2013, through Interscope Records. It was released in the United States on March 11, 2014, and April 7, 2014, in the United Kingdom. The album has charted in Austria, Germany and Switzerland. It includes production and co-songwriting from DJ Khalil, Pharrell Williams, Elton John, Theron Feemster and Rock Mafia. Strings for the entire album were arranged and recorded by Daniel "Danny Keyz" Tannenbaum. The album received a nomination for the Grammy Award for Best R&B Album at the 57th Grammy Awards in 2015.

Aloe Blacc
Egbert Nathaniel Dawkins III (born January 7, 1979), known professionally as Aloe Blacc (/ˈæloʊ ˈblæk/ ⓘ), is an American singer, songwriter, rapper, and record producer. He is known for his guest performance on Avicii's 2013 single "Wake Me Up", which topped the charts in 22 countries, including in Australia and the UK. As a lead artist, he is known for his singles "I Need a Dollar" and "The Man", the latter of which reached number one on the UK Singles Chart. Aside from his solo career, Aloe Blacc is also a member of the hip hop duo Emanon, alongside American record producer Exile.
Hell Gates
Hell Gates (62°40′20.3″S 61°10′46.4″W﻿ / ﻿62.672306°S 61.179556°W﻿ / -62.672306; -61.179556) is a narrow (20 m wide) boat passage between the Vardim Rocks and Devils Point on Byers Peninsula, connecting Raskuporis Cove and Osogovo Bay at the southwest end of Livingston Island in the South Shetland Islands, Antarctica. The name dates back to about 1821 and was applied by early sealers in the area because many lives and ships were lost here.

Livingston Island
Livingston Island (Russian name Smolensk, 62°36′S 60°30′W﻿ / ﻿62.600°S 60.500°W﻿ / -62.600; -60.500) is an Antarctic island in the Southern Ocean, part of the South Shetlands Archipelago, a group of Antarctic islands north of the Antarctic Peninsula. It was the first land discovered south of 60° south latitude in 1819, a historic event that marked the end of a centuries-long pursuit of the mythical Terra Australis Incognita and the beginning of the exploration and utilization of real Antarctica. The name Livingston, although of unknown derivation, has been well established in international usage since the early 1820s.
William Hunter (surgeon)
William Hunter CB FRSE (1 June 1861 – 13 January 1937) was a British surgeon known primarily for his theories on oral sepsis, one of the inspirations for the Henry Cotton theory of focal sepsis which led to the increased number of tooth extractions and tonsillectomies in the 1910s and 20s (under the presumption that hidden sepsis could lead to a wider health decline in individuals). By the 1930s, this view had fallen out of favor, but not until after thousands of surgeries had been performed.

Order of St. Sava
The Order of St. Sava (Serbian: Орден Светог Саве, romanized: Orden Svetog Save) is an ecclesiastic decoration conferred by the Serbian Orthodox Church and a dynastic order presented by the house of Karađorđević. It was previously a state order awarded by both the Kingdom of Serbia and the Kingdom of Serbs, Croats and Slovenes/Kingdom of Yugoslavia.

The state order was awarded to nationals and foreigners for meritorious achievements in the field of religion, education, science and the arts as well as for social and relief work. It was abolished in 1945 with the proclamation of the People’s Federal Republic of Yugoslavia and the end of the monarchy, while continuing as a dynastic order, with appointments currently made by Alexander, Crown Prince of Yugoslavia.

The ecclesiastic order is awarded to ecclesiastic and secular persons with special merits.
Sherali Dostiev
Sherali Dostiev (Шерали Достиев; born January 12, 1985, in Dushanbe, Region of Republican Subordination) is a male boxer from Tajikistan. He is competing in the Light Flyweight (– 48 kg) division, and won a bronze medal at the 2005 World Amateur Boxing Championships.

He competed at the 2004 Summer Olympics, but was knocked out in the round of 32 by Harry Tanamor of the Philippines. Dostiev qualified for the Athens Games by ending up in first place at the 1st AIBA Asian 2004 Olympic Qualifying Tournament in Guangzhou, PR China. In the final he defeated Thailand's Suban Pannon.

In 2008 he lost 1:12 to Cuban Yampier Hernández.

1st AIBA Asian 2004 Olympic Qualifying Tournament
The 1st AIBA Asian 2004 Olympic Boxing Qualifying Tournament was held in Guangzhou, PR China from March 18 to March 23, 2004. It was the first chance for amateur boxers from Asia to qualify for the 2004 Summer Olympics after the 2004 Asian Amateur Boxing Championships in Puerto Princesa, Philippines from January 11 to 18, 2004. The top two boxers in each weight division gained a place in the Olympics, with the exception of the heavyweight and super heavyweight divisions in which just the winner was entered.
Embodiment 12:14
Embodiment 12:14 were an Australia Christian metal band formed in Adelaide, as Embodiment in 1992, initially they performed death metal. They released two albums, Elements of This Man-Made Man (1998) and Inroads Out (2005), before disbanding in 2006.

Trial & Error Records
Trial & Error Records is an independent record label based in Melbourne, Victoria. It is one of Australia's largest hardcore labels. The label is owned and run by Mindsnare bassist, Nigel Melder. As of 2019 Trial and Error are no longer releasing music.
Mikolin
Mikolin [miˈkɔlin] is a village in the administrative district of Gmina Lewin Brzeski, within Brzeg County, Opole Voivodeship, in south-western Poland.

The name of the village comes from the name Mikołaj (Nicholas).

During World War II, on 21 January 1945, a German-organized death march of Allied prisoners of war from the Stalag Luft 7 POW camp passed through the village.

Stalag Luft 7
Stalag Luft 7 was a World War II Luftwaffe prisoner-of-war camp located in Morzyczyn, Pomerania, and Bankau, Silesia (now Bąków, Poland). It held British, Canadian, Australian, New Zealander, French, Polish, South African, American and other Allied airmen.
Milagros: Girl from Away
Milagros: Girl from Away is a 2008 children's novel by Cuban-American author Meg Medina. It was first published on 11 November 2008 through Henry Holt and Company and follows a young girl who has to deal with various struggles, including an absentee father. The book took Medina about eighteen months to write.

Meg Medina
Meg Medina is an American children’s book author of Cuban descent whose books celebrate Latino culture and the lives of young people. She served as the 2023–2024 National Ambassador for Young People’s Literature. Medina is the recipient of the 2019 John Newbery Medal for her middle grade novel, Merci Suárez Changes Gears and the Pura Belpré Award for Yaqui Delgado Wants to Kick Your Ass (2014) and the Pura Belpré Award Honor Book in 2016 for Mango, Abuela and Me).
Barazoku
Barazoku (薔薇族) was Japan's first commercially circulated gay men's magazine. It began publication in July 1971 by Daini Shobō's owner's son and editor Bungaku Itō (伊藤 文學, Itō Bungaku), although before that, there had been Adonis and Apollo, its extra issue, around 1960 serving as a members-only magazine. Barazoku was Japan's oldest and longest-running monthly magazine for gay men. However, it halted publication three times due to the publisher's financial hardships. In 2008, Itō announced that the 400th issue would be the final one. The title means "the rose tribe" in Japanese, hinted from King Laius' homosexual episodes in Greek mythology. The magazine was printed in Japanese only. Barazoku's Bungaku Itō coined the term for the Japanese lesbian community as ("lily tribe") which the slang term for lesbian yuri comes from.

Ito Bungaku
Bungaku Ito (Jap. 伊藤 文學 new characters 伊藤 文学; born March 19, 1932) is a Japanese entrepreneur, founder and editor-in-chief of Japan's first commercially based homosexuality magazine Barazoku. He is the president of Daini-Shobo (Jap. 株式会社第二書房).
Valley View, Wichita County, Texas
Valley View is an unincorporated community in Wichita County, Texas, United States. It has an estimated population of 200.

Valley View is part of the Wichita Falls, Texas Metropolitan Statistical Area.

Wichita County, Texas
Wichita County (/ˈwɪtʃɪtɔː/ WITCH-ih-taw) is a county located in the U.S. state of Texas. As of the 2020 census, its population was 129,350. The county seat is Wichita Falls. The county was created in 1858 and organized in 1882. Wichita County is part of the Wichita Falls, Texas, TX metropolitan statistical area.
Bad Homburg Open
The Bad Homburg Open is a women's professional tennis tournament held on outdoor grass courts at the Bad Homburg Tennis Club in Bad Homburg, Germany. The event held its inaugural edition in June 2021 after it was initially postponed from 2020 due to the COVID-19 pandemic.

In September 2019, the All England Lawn Tennis and Croquet Club (AELTC) announced that they would invest in new grass tennis tournaments to be scheduled before the Wimbledon Championships on the ATP Tour and WTA Tour. Among the new investments included a WTA event planned for Bad Homburg with the collaboration of German sports agency Perfect Match as well as German tennis player Angelique Kerber and her management team, after which she would become the tournament ambassador. The new stadium at the Bad Homburg Tennis Club was built on the site of the first tennis court in continental Europe, Kurpark, and in July 2020, Kerber christened the stadium at its opening ceremony.

Angelique Kerber
Angelique Kerber (German: [ʔan.d͡ʒɛˈliːk ˈkɛɐ̯bɐ] ⓘ; born 18 January 1988) is a German former professional tennis player. She was ranked as the world No. 1 in women's singles by the Women's Tennis Association (WTA) for 34 weeks, including as the year-end No. 1 in 2016. Kerber won 14 WTA Tour-level singles titles, including three majors at the 2016 Australian Open, 2016 US Open, and 2018 Wimbledon Championships. She also won a silver medal in women's singles at the 2016 Rio Olympics.

An accomplished left-handed player, Kerber made her professional debut in 2003 and came to prominence by reaching the semifinals of the 2011 US Open as the world No. 92. Kerber first cracked the top 5 in the rankings in 2012 and would eventually become the world No. 1 on 12 September 2016, becoming the 22nd and oldest player to achieve the top ranking for the first time. Following a maternity leave, Kerber retired from the sport after the 2024 Paris Olympics.
Frelinghuysen Morris House and Studio
The Frelinghuysen Morris House and Studio is a historic house museum and former art studio in Lenox and Stockbridge, Massachusetts.  The house and studio were home to American Abstract Artists George L.K. Morris and Suzy Frelinghuysen. The studio was built in Bauhaus style in 1930 by Morris and his friend George Sanderson. The house was added in 1941, designed by John Butler Swann. The house and studio were entered onto the National Register of Historic Places in 2016.

The house contains furnishings and decorations unchanged since the couple's lifetime. The art collection includes cubist frescoes and paintings by Morris and Frelinghuysen, as well as works by Pablo Picasso, Juan Gris, Georges Braque, Joan Miró and Henri Matisse.

Lenox, Massachusetts
Lenox is a town in Berkshire County, Massachusetts, United States. The town is in Western Massachusetts and part of the Pittsfield Metropolitan Statistical Area. The population was 5,095 at the 2020 census. Lenox is the site of Shakespeare & Company and Tanglewood, summer home of the Boston Symphony Orchestra. Lenox includes the villages of New Lenox and Lenox Dale and the census-designated place of Lenox, and is a tourist destination during the summer.
Pierre de Villars
Pierre de Villars (1623, Paris - 20 March 1698, Paris), known by courtesy as the Marquis de Villars, was a French diplomat and Councillor of State.

He was the son of Claude de Villars, mestre de camp and gentleman of the King's bedchamber, and of his wife Charlotte Louvet de Nogaret-Calvisson, and grandson of René of Savoy, known as the Bastard of Savoy (Bâtard de Savoie), and thus (illegitimately) the great-grandson of Philip II, Duke of Savoy.

He was married to Marie Gigault de Bellefonds and they had two sons, Armand (died 1712) and Claude-Louis-Hector (1653–1734) who inherited his father's title, Marquis de Villars.

Between 1679 and 1681, Villars and his wife were assigned to the royal court in Madrid to represent French King Louis XIV to Spanish King Charles II and his new French-born wife: Marie Louise d'Orléans, the young and beautiful niece of Louis XIV.

Charles II of Spain
Charles II (6 November 1661 – 1 November 1700) was the king of Spain from 1665 to 1700. The last monarch from the House of Habsburg that had ruled Spain since 1516, his death without children resulted in the 1701 to 1714 War of the Spanish Succession.

For reasons still debated, Charles experienced lengthy periods of ill health throughout his life. This made the question of who would succeed him central to European diplomacy for much of his reign, with one historian writing that "from the day of his birth, they were waiting for his death".

The two candidates for the succession were Charles of Austria, from the House of Habsburg, and Philip of Anjou, the 16-year-old grandson of Louis XIV of France, from the House of Bourbon. Shortly before dying in November 1700, Charles made the latter his heir, but the acquisition of an undivided Spanish Empire by either threatened the European balance of power and resulted in war.
Bräcke Municipality
Bräcke Municipality (Swedish: Bräcke kommun) is a municipality in Jämtland County in northern Sweden. Its seat is located in Bräcke.

The present municipality was formed in 1974 when "old" Bräcke Municipality was amalgamated with Kälarne and Revsund. The three former municipalities had been created in 1952. The number of original entities (as of 1863) were six. Due to the declining population in the area further amalgamations have been proposed, but rejected.

Bräcke
Bräcke is a locality and the seat of Bräcke Municipality in Jämtland County, Sweden with 1,651 inhabitants as of 2010.

The community is located next to Lake Revsundssjön, 70 km south-east of Östersund.   
The railway has been an important factor in Bräcke's development. The town is located along the Central line and serves as the starting point of the Main Line Through Upper Norrland. European route E14 also passes through Bräcke and Länsväg 323 starts in Bräcke and goes towards Kälarne.

Bräcke Church (Bräcke kyrka) was built in the summer of 1859 following a drawing by Abraham Rafael Ulric Pettersson (1824-1866). The church building is externally clad with white painted wooden paneling. The ceiling of the church room has a thin vault of wood.  The altarpiece was painted in 1926 by Stockholm artist Karl Tirén (1869-1955).  In the church tower hang two bells; the little bell was cast in 1778 and  large bell was cast in 1859.
Burapha University Hospital
Burapha University Hospital (Thai: โรงพยาบาลมหาวิทยาลัยบูรพา) is a university teaching hospital, affiliated to the Faculty of Medicine of Burapha University, located in Mueang Chonburi District, Chonburi Province. It is a hospital capable of super tertiary care.

Faculty of Medicine, Burapha University
The Faculty of Medicine, Burapha University (Thai: คณะแพทยศาสตร์ มหาวิทยาลัยบูรพา) is the first medical school in Eastern Thailand, located in Mueang Chonburi District, Chonburi Province. It is part of the group of Health Science Faculties of Bangsaen Campus.
Jane Seymour (Canadian actress)
Jane Seymour (born Marjorie Seymour Fitz-patrick; March 24, 1893 – January 30, 1956) was a Canadian-American film and television actress known for her performance in films including playing mom in Tom, Dick and Harry (1941) and for roles in several TV series.

Tom, Dick and Harry (1941 film)
Tom, Dick and Harry is a 1941 RKO Radio Pictures American comedy film written by Paul Jarrico, directed by Garson Kanin and starring Ginger Rogers, George Murphy, Alan Marshal, Phil Silvers and Burgess Meredith. Rogers was working on the film when she was awarded the Academy Award for Best Actress for her performance in Kitty Foyle (1940).

Tom, Dick and Harry was remade as The Girl Most Likely (1957), a musical that was also the last film released by RKO.
Scrambled Wives
Scrambled Wives is a lost 1921 American silent comedy film produced by and starring Marguerite Clark. It was directed by Edward H. Griffith and released through Associated First National. This film had one color sequence, presumably a 1-strip Technicolor process being that Technicolor's Ray June is one of the cameramen. This film marks Clark's final screen performance. It is not known whether the film currently survives. 
This film is based on the play The First Mrs. Chiverick by Adelaide Matthews.

Edward H. Griffith
Edward H. Griffith (August 23, 1888 – March 3, 1975) (also known as E H Griffith, Lieut. Edward H. Griffith, Edward Griffith, and E. H. Griffith) was an American motion picture director, screenwriter, and producer.
Declan Lowney
Declan Lowney (born 23 April 1960) is an Irish television and film director. Known initially for directing musical events such as the 1988 Eurovision Song Contest, Lowney has also directed Irish and British television comedies, including Cold Feet and Little Britain. He won a BAFTA Award in 1995 for directing Father Ted. He was awarded a second BAFTA Award in 2006 for his work on BBC comedy Help.

He has directed two feature films, Wild About Harry in 2000, and Alan Partridge: Alpha Papa in 2013.

Wild About Harry (2000 film)
Wild About Harry is a 2000 British comedy film directed by Declan Lowney and written by Colin Bateman. The film stars Brendan Gleeson, Amanda Donohoe, James Nesbitt, Adrian Dunbar, Bronagh Gallagher and Ruth McCabe. The film was released on 26 October 2001 by United International Pictures.
A jj 12″
a jj 12″ is an EP by the Swedish band JJ, released on their label Sincerely Yours in December 2009. It consists of two songs from jj n° 2, "from africa to málaga" and "intermezzo", and two previously unreleased songs, "baby" and "the truth". A video for the song "baby", directed by Marcus Söderlund featuring slow-motion footage of horses, was released on the Sincerely Yours website. It was released as a 12″ vinyl in a limited amount and made available for download.

JJ (Swedish band)
JJ, styled as jj, is a Swedish band who has released music through the Gothenburg-based independent label Sincerely Yours and the Bloomington, Indiana-based label Secretly Canadian. The band consists of Joakim Benon and Elin Kastlander.
José Antônio Peruzzo
José Antônio Peruzzo (born 19 April 1960) is a Brazilian prelate of the Catholic Church who has been Archbishop of Curitiba since January 2015. He was Bishop of Palmas–Francisco Beltrão from 2005 to 2015.

Archdiocese of Curitiba
There is also a Diocese of Curitiba (and a Bishop of Curitiba) in the Anglican Episcopal Church of Brazil.

The Roman Catholic Archdiocese of Curitiba (Latin: Archidioecesis Curitibensis) is a Latin Rite Metropolitan archdiocese in Paraná, southern Brazil.

Its cathedral archiepiscopal see is a Minor Basilica: Catedral Metropolitana Basílica Nossa Senhora da Luz dos Pinhais, dedicated to Our Lady of the Candles, in Curitiba.