OpenLLM-France/wikimedia huggingface dataset:
# Seth Evans

Seth Evans is a scholar and educator who specializes in the Abhidhamma Pitaka (abhidhammapiṭaka) and the Visuddhimagga. He is known for his work in the phenomenological aspects of Buddhist psychology. Evans also plays bass for the punk-rock band The Out of Sorts.

## Biography

Evans was born in Denver, Colorado. He started his career as the bass player for the Denver-based punk rock band Reno Divorce and toured America and Europe. After ordaining as a monk, he completed his graduation in Buddhist theory as a Theravada monk at Mahachulalongkornrajavidyalaya University. As a monk, he taught meditation at Wat Prayong where he completed five vassa. His academic focus was primarily on Buddhist ontology, Buddhist metaphysics, and Buddhist epistemology. He completed his PhD in Philosophy from Assumption University of Thailand.
Evans teaches Buddhist philosophy at Mahachulalongkornrajavidyalaya University. He is also chief editor of Journal of International Association of Buddhist Universities.
As a Buddhist scholar, Evans cautions against understanding the teachings of the traditional Buddha of the Pāli Canon with modern scientific concepts such as material cause and effect in terms of karma, neurology in regards to citta, and the scientific method as understood in the 21st century in general. Instead, he urges a hermeneutic interpretation of the Pāli Canon within the context of the North-Indian culture of 2,500 years ago. In 2018, he joined the Bangkok punk rock band The Out of Sorts as their bass player.

## Articles

* Conditions and Appearance: Exploring the Translations of Rūpa in the Mahānidāna Sutta
* The Buddha's Temperance: A Comparison of Epicureanism and the Dhamma
* Individualism and the Kālāmas: Critiques of American Buddhism
# Hilbert–Speiser theorem

In mathematics, the Hilbert–Speiser theorem is a result on cyclotomic fields, characterising those with a normal integral basis. More generally, it applies to any finite abelian extension of Q, which by the Kronecker–Weber theorem are isomorphic to subfields of cyclotomic fields.
    Hilbert–Speiser Theorem. A finite abelian extension K/Q has a normal integral basis if and only if it is tamely ramified over Q.
This is the condition that it should be a subfield of Q(ζ$_n$) where n is a squarefree odd number. This result was introduced by Hilbert (1897, Satz 132, 1998, theorem 132) in his Zahlbericht and by Speiser (1916, corollary to proposition 8.1).
In cases where the theorem states that a normal integral basis does exist, such a basis may be constructed by means of Gaussian periods. For example if we take n a prime number p > 2, Q(ζ$_p$) has a normal integral basis consisting of all the p-th roots of unity other than 1. For a field K contained in it, the field trace can be used to construct such a basis in K also (see the article on Gaussian periods). Then in the case of n squarefree and odd, Q(ζ$_n$) is a compositum of subfields of this type for the primes p dividing n (this follows from a simple argument on ramification). This decomposition can be used to treat any of its subfields.
Cornelius Greither, Daniel R. Replogle, and Karl Rubin et al. (1999) proved a converse to the Hilbert–Speiser theorem:
    Each finite tamely ramified abelian extension K of a fixed number field J has a relative normal integral basis if and only if J =Q.
There is an elliptic analogue of the theorem proven by Anupam Srivastav and Martin J. Taylor (1990). It is now called the Srivastav-Taylor theorem (1996).
# Milan Kolena

Milan Kolena (born May 12, 1994) is a Slovak ice hockey centre. He most recently played for the Sheffield Steeldogs of the National Ice Hockey League in the United Kingdom.
Kolena previously played nine games in the Kontinental Hockey League for HC Slovan Bratislava and also played in the Slovak Extraliga for MHC Martin, HC Košice, MsHK Žilina and ŠHK 37 Piešťany.
He moved to the United Kingdom in 2016, signing for the Telford Tigers.

## Career statistics
### International

| Year | Team | Event | GP | G | A | Pts | PIM |
| 2012 | Slovakia | U18 D1A | 5 | 3 | 5 | 8 | 2 |
| 2013 | Slovakia | WJC | 6 | 0 | 3 | 3 | 2 |
| 2014 | Slovakia | WJC | 5 | 4 | 4 | 8 | 6 |
| WJC totals | WJC totals | WJC totals | 11 | 4 | 7 | 11 | 8 |
# Kuriyama, Tochigi

Kuriyama (栗山村, Kuriyama-mura) was a village located in Shioya District, Tochigi Prefecture, Japan.
As of 2003, the village had an estimated population of 2,068 and a density of 4.84 persons per km$^2$. The total area was 427.37 km$^2$.
On March 20, 2006, Kuriyama, along with the city of Imaichi, the town of Ashio (from Kamitsuga District), and the town of Fujihara (also from Shioya District), was merged into the expanded city of Nikkō. As a result of the merger, no villages remain in Tochigi Prefecture.
# Kenny Evans (high jumper)

Kenny Evans (born April 6, 1979) is a retired American high jumper. He finished thirteenth at the 2000 Olympic Games. His personal best jump is 2.31 metres (7 ft 7 in), achieved in March 2000 in Fayetteville.
Evans won the high jump at the 1998 and 2001 NCAA Indoor Track and Field Championships. He was also a three-time champion indoors and a winner outdoors at the Southeastern Conference Championships.
Evans is the father of professional basketball player Keenan Evans, who previously played college basketball at Texas Tech University.
# St. Louis Literary Award

The St. Louis Literary Award has been presented yearly since 1967 to a distinguished figure in literature. It is sponsored by the Saint Louis University Library Associates.

## Winners

Past Recipients of the Award:
* 2025 Colson Whitehead
* 2024 Jamaica Kincaid
* 2023 Neil Gaiman
* 2022 Arundhati Roy
* 2021 Zadie Smith
* 2020 Michael Chabon
* 2019 Edwidge Danticat
* 2018 Stephen Sondheim
* 2017 Margaret Atwood
* 2016 Michael Ondaatje
* 2015 David Grossman
* 2014 Jeanette Winterson
* 2013 [no award]
* 2012 Tony Kushner
* 2011 Mario Vargas Llosa
* 2010 Don DeLillo
* 2009 Sir Salman Rushdie
* 2008 E. L. Doctorow
* 2007 William H. Gass
* 2006 Michael Frayn
* 2005 Richard Ford
* 2004 Garry Wills
* 2003 Margaret Drabble
* 2002 Joan Didion
* 2001 Simon Schama
* 2000 N. Scott Momaday
* 1999 Chinua Achebe
* 1998 Seamus Heaney
* 1997 Stephen E. Ambrose
* 1996 Antonia Fraser
* 1995 Edward Albee
* 1994 Stephen Jay Gould
* 1993 David McCullough
* 1992 Shelby Foote
* 1991 August Wilson
* 1990 Tom Wolfe
* 1989 Richard Wilbur
* 1988 Joyce Carol Oates
* 1987 John Updike
* 1986 Saul Bellow
* 1985 Walker Percy
* 1984 [no award]
* 1983 Eudora Welty
* 1982 William Styron
* 1981 James A. Michener
* 1980 Arthur Miller
* 1979 Howard Nemerov
* 1978 Mortimer J. Adler
* 1977 Robert Penn Warren
* 1976 R. Buckminster Fuller
* 1975 John Hope Franklin
* 1974 Tennessee Williams
* 1973 James T. Farrell
* 1972 Francis Warner
* 1971 Barbara Tuchman
* 1970 W. H. Auden
* 1969 George Plimpton
* 1968 Jacques Barzun
* 1967 Henry Steele Commager
# Holy Trinity Church, Eskişehir

The Holy Trinity Church (Turkish: Kutsal Üçlü Ermeni Kilisesi, Armenian: Սուրբ Երրորդություն եկեղեցի) or Surp Yerrortut'yun Church is a historical Armenian Apostolic temple in the former Armenian quarter called Hoshnudiye (nowadays Tepebaşı) of the Western Turkish town of Eskishehir. It was turned into an adult theater after the Armenians of the town were deported and killed during the Armenian genocide.
The church was built in the 19th century. After the Armenian genocide in 1915, the church was sold by the Turkish state and used as the Asri Cinema of 1945 which showed sex movies only after 1974. A restoration plan started in 2009. The church building is currently used as the Zübeyde Hanım Cultural Centre named after the mother of the founding father of Turkey, Mustafa Kemal Atatürk.

## Sources

* "Eskişehir'de Hırant Dink Anıldı" (in Turkish). 18 January 2015. Retrieved 7 August 2015. (in Turkish)
* "İşte çözemediğimiz problem" (in Turkish). 5 November 2008. Retrieved 7 August 2015. (in Turkish)
vte Eskişehir Province :
Settlements :
Culture :
Buildings and structures :
Eskişehir Province :
39°46′38″N 30°31′09″E﻿ / ﻿39.7771°N 30.5191°E﻿ / 39.7771; 30.5191
* This article about a church building or other Christian place of worship in Turkey is a stub. You can help Wikipedia by expanding it.
* v
* t
* e
* This article on an Armenian Apostolic church building is a stub. You can help Wikipedia by expanding it.
* v
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# Flatow Amendment

The Flatow Amendment is an amendment to the Foreign Sovereign Immunities Act of 1976 passed in 1996, which allows American victims of terrorism to sue countries that are designated as terrorism sponsors. The legislation establishes that foreign state sponsors of terrorism "shall be liable to a United States national … for personal injury or death caused by acts of that [party]…."
It is named after Stephen Flatow, whose daughter Alisa Flatow was killed in a suicide bombing attack carried out by militants belonging to the Islamic Jihad Movement in Palestine in 1995. After her death, Flatow commenced a series of lawsuits against the Iranian government.
US Courts are thus authorized to award money damages to said victims. The executive branch, however, has often resisted paying these judgments from frozen terrorist state assets by arguing that it would hamper presidential ability to conduct foreign affairs.
# Ahmed Belal (handballer)

Ahmed Belal (born March 12, 1968) is an Egyptian handball player. He competed for Egypt's national team at the 1992, 1996 and 2000 Summer Olympics.
# Don Hammond (Australian footballer)

Don Hammond (24 August 1922 – 16 July 2005) was an Australian rules footballer who played with Fitzroy in the Victorian Football League (VFL).
# Terence Farrell

Terence Farrell (1798 – 19 March 1876) was an Irish sculptor, now best known for his portrait busts and works at Wrest Park for Earl de Grey.
Farrell was born in Creve, County Longford, and in 1810 brought to Dublin and enrolled in the Modelling School of the Dublin Society, where he studied under Edward Smyth and later John Smyth. After school, he entered Thomas Kirk's studio, where he continued his studies for nearly seven years as a pupil, and subsequently as an assistant. In 1826 he made his first contribution to the Royal Hibernian Academy, and about 1828 he established his own workshop. He exhibited regularly in the Academy, where he was elected an Associate in July, 1851, and a Member in May, 1859. He is buried in St Andrew's Church, Westland Row, Dublin.

## Selected works

* Sir Lowry Cole. Statue in Portland stone, Enniskillen.
* William, 3rd Earl of Enniskillen. Statue, Enniskillen Church.
* Lt.-Col. Tomlinson. Monument erected by the officers of the 18th Royal Irish Regiment, St. Patrick's Cathedral, 1853.
* Sir Hussey Vivian, Commander of the Forces. Monument, Truro Church, Cornwall.
* Early Affliction. Marble Statue. R.H.A., 1848.
* The Seasons, Wrest Park.
# Coupé (carriage)

A coupé was a four-wheeled carriage with outside front seat for the driver and enclosed passenger seats for two persons. The name coupé comes from the French past participle of couper, "cut".
The coupé carriage body style originated from the berline horse-drawn carriage. The coupé version of the berline was introduced in the 18th century as a shortened ("cut") version with no rear-facing seat. Normally, a coupe had a fixed glass window in the front of the passenger compartment. The coupe was considered an ideal vehicle for women to use to go shopping or to make social visits.

## Types

The grand coupé with a curved body was the first common form of this carriage. Around 1830, the small coupé appeared, of four wheels, a closed squared body, with seats for two passengers. The coachman's seat, at the front and outside, rests on a chest. The small coupé is suspended on two pincer springs at the front and half-pincer springs at the rear, connected by a transverse spring. The small coupé was the model of the French fiacre.
There are a number of coupé types, including but not limited to:
* Town coupé: a prestigious two-seater carriage, reserved for ceremonies.
* Mail coupé: derived from the English-style mail coach, and retained the exterior seats and trunks.
* Chariot: a type of curved light coupé.
* Brougham: a type of squared small coupé.
* Three-quarter coupé or Clarence: a coupé with a projecting glass front and seats for four passengers inside.
* Landaulet: the coupé form of the landau. There are also the brougham-landaulet and the three-quarter landaulet.
* Dorsay: a boat-shaped double-suspension coupé.
The coupé also refers to the front part of a composite carriage, such as a diligence (Continental-style stagecoach).
# Ralstonia pickettii

Ralstonia pickettii is a Gram-negative, rod-shaped, soil bacterium.
Ralstonia pickettii is a Betaproteobacteria species found in moist environments such as soils, rivers, and lakes. It has also been identified in biofilms in plastic water pipes. It is an oligotrophic organism, making it capable of surviving in areas with a very low concentration of nutrients. Several strains have shown an ability to survive in environments highly contaminated with metals. The ability to persist in these harsh conditions makes R. pickettii a candidate for bioremediation.
Ralstonia pickettii and R. insidiosa are emerging pathogens in hospital settings. R. pickettii pathology does not follow an easy definition. Several hospitals have reported outbreaks—in particular, patients with cystic fibrosis and Crohn's disease have been shown to be infected with R. picketti. Of the 55 reported cases of such infection, the majority are due to contaminated solutions such as water, saline, and sterile drugs. These solutions are usually contaminated when the product is manufactured, because R. pickettii has the ability to pass through 0.45 and 0.2 μm filters that are used to sterilize medicinal products. An outbreak of R. pickettii at a hospital in Queensland, Australia was reported in November 2023, and it is suspected to have caused the death of one patient through contaminated saline.
The majority of R. pickettii and R. insidiosa isolates showed susceptibility to most of the antibiotics tested. The most effective were found to be the quinolones and sulfamethoxazole/trimethoprim. The two bacterial species can be difficult to tell apart.
# Lukáš Paukovček

Lukáš Paukovček (born 13 November 1990) is a Slovak professional ice hockey player who currently playing for Vlci Žilina of the Slovak 1. Liga.

## Career statistics
### Regular season and playoffs

| | | | Regular season | Regular season | Regular season | Regular season | Regular season | Playoffs | Playoffs | Playoffs | Playoffs | Playoffs |
| Season | Team | League | GP | G | A | Pts | PIM | GP | G | A | Pts | PIM |
| 2008–09 | MHk 32 Liptovský Mikuláš | Slovak-Jr. | 48 | 13 | 20 | 33 | 146 | — | — | — | — | — |
| 2008–09 | MHk 32 Liptovský Mikuláš | Slovak | 2 | 0 | 0 | 0 | 0 | — | — | — | — | — |
| 2009–10 | MHk 32 Liptovský Mikuláš | Slovak-Jr. | 33 | 20 | 16 | 36 | 82 | — | — | — | — | — |
| 2009–10 | MHk 32 Liptovský Mikuláš | Slovak | 5 | 0 | 0 | 0 | 0 | — | — | — | — | — |
| 2010–11 | MHk 32 Liptovský Mikuláš | Slovak-Jr. | 8 | 9 | 4 | 13 | 2 | 1 | 0 | 0 | 0 | 0 |
| 2010–11 | MHk 32 Liptovský Mikuláš | Slovak.1 | 14 | 4 | 6 | 10 | 24 | 12 | 5 | 2 | 7 | 20 |
| 2011–12 | MHk 32 Liptovský Mikuláš | Slovak.1 | 42 | 14 | 16 | 30 | 86 | 1 | 0 | 1 | 1 | 0 |
| 2012–13 | MHk 32 Liptovský Mikuláš | Slovak.1 | 38 | 20 | 24 | 44 | 62 | 5 | 2 | 5 | 7 | 46 |
| 2013–14 | HK Poprad | Slovak | 46 | 5 | 13 | 18 | 24 | 4 | 0 | 1 | 1 | 2 |
| 2014–15 | HK Poprad | Slovak | 54 | 7 | 17 | 24 | 126 | 12 | 3 | 3 | 6 | 8 |
| 2015–16 | HK Poprad | Slovak | 54 | 13 | 14 | 27 | 88 | 4 | 1 | 0 | 1 | 4 |
| 2016–17 | HK Nitra | Slovak | 52 | 4 | 9 | 13 | 89 | 13 | 3 | 2 | 5 | 16 |
| 2017–18 | MHk 32 Liptovský Mikuláš | Slovak | 44 | 5 | 11 | 16 | 40 | — | — | — | — | — |
| 2018–19 | HK Poprad | Slovak | 49 | 11 | 19 | 30 | 74 | 12 | 1 | 2 | 3 | 28 |
| 2019–20 | HK Poprad | Slovak | 33 | 5 | 6 | 11 | 30 | — | — | — | — | — |
| 2019–20 | HK Dukla Trenčín | Slovak | 17 | 7 | 7 | 14 | 68 | — | — | — | — | — |
| 2020–21 | HK Dukla Trenčín | Slovak | 41 | 9 | 21 | 30 | 42 | 10 | 3 | 5 | 8 | 16 |
| 2021–22 | HK Dukla Trenčín | Slovak | 35 | 6 | 13 | 19 | 22 | — | — | — | — | — |
| 2021–22 | HC '05 Banská Bystrica | Slovak | 9 | 0 | 1 | 1 | 6 | 6 | 0 | 0 | 0 | 6 |
| 2022–23 | HK Poprad | Slovak | 33 | 3 | 3 | 6 | 20 | — | — | — | — | — |
| Slovak totals | Slovak totals | Slovak totals | 474 | 75 | 134 | 209 | 629 | 61 | 11 | 13 | 24 | 80 |
# Amer Serageldin

Amer Serageldin (born July 1, 1971) is an Egyptian handball player. He competed for Egypt's national team at the 1992 Summer Olympics.
# Maurie Edwards

Maurice Cooper Edwards (17 October 1922 – 26 February 2007) was an Australian rules footballer who played with Essendon and North Melbourne in the Victorian Football League (VFL).
Edwards served in the Australian Army during World War II.
# Vernon Sasso

Vernon Sasso (born 10 February 1897, date of death unknown) was a Jamaican cricketer. He played in one first-class match for the Jamaican cricket team in 1929/30.
# Lyubomir Chernev

Lyubomir Chernev (Bulgarian: Любомир Чернев) (born 27 May 1986) is a Bulgarian football player, currently playing for Chavdar Byala Slatina as a midfielder. Chernev is a left midfielder. His first club was Sportist Svoge.
# Multiplicity-one theorem

In the mathematical theory of automorphic representations, a multiplicity-one theorem is a result about the representation theory of an adelic reductive algebraic group. The multiplicity in question is the number of times a given abstract group representation is realised in a certain space, of square-integrable functions, given in a concrete way.
A multiplicity one theorem may also refer to a result about the restriction of a representation of a group G to a subgroup H. In that context, the pair (G, H) is called a strong Gelfand pair.

## Definition

Let G be a reductive algebraic group over a number field K and let A denote the adeles of K. Let Z denote the centre of G and let ω be a continuous unitary character from Z(K)\Z(A)$^×$ to C$^×$. Let L$^2$$_0$(G(K)/G(A), ω) denote the space of cusp forms with central character ω on G(A). This space decomposes into a direct sum of Hilbert spaces
    $L_{0}^{2}(G(K)\backslash G(\mathbf {A} ),\omega )={\widehat {\bigoplus }}_{(\pi ,V_{\pi })}m_{\pi }V_{\pi }$
where the sum is over irreducible subrepresentations and m$_π$ are non-negative integers.
The group of adelic points of G, G(A), is said to satisfy the multiplicity-one property if any smooth irreducible admissible representation of G(A) occurs with multiplicity at most one in the space of cusp forms of central character ω, i.e. m$_π$ is 0 or 1 for all such π.

## Results

The fact that the general linear group, GL(n), has the multiplicity-one property was proved by Jacquet & Langlands (1970) for n = 2 and independently by Piatetski-Shapiro (1979) and Shalika (1974) for n > 2 using the uniqueness of the Whittaker model. Multiplicity-one also holds for SL(2), but not for SL(n) for n > 2 (Blasius 1994).

## Strong multiplicity one theorem

The strong multiplicity one theorem of Piatetski-Shapiro (1979) and Jacquet and Shalika (1981a, 1981b) states that two cuspidal automorphic representations of the general linear group are isomorphic if their local components are isomorphic for all but a finite number of places.
# Aleksandar Miljković (footballer, born 1982)

Aleksandar Miljković (Serbian Cyrillic: Александар Mиљкoвић; born 23 August 1982) is a Serbian retired football midfielder who primarily played for hometwown club FK Smederevo in the Serbian First League.
He also played with FK Železničar Smederevo and INON Požarevac and had a spell in Myanmar.
# Ashraf Mabrouk Awaad

Ashraf Mabrouk Awaad (born June 1, 1972) is an Egyptian handball player. He competed for Egypt's national team at the 1992, 1996, 2000 Summer Olympics.
His brothers, Hazem, Hussein, Belal, Ibrahim and Hassan, are also international handball players.
# Terry Healy

John Terrence Healy (2 July 1921 – 30 April 2009) was an Australian rules footballer who played with Essendon in the Victorian Football League (VFL).
# Qurqania

Qurqania (Arabic: قُورْقَانِيَا, romanized: Qūrqāniyā, also spelled Qurqanya or Korkania) is a town in Syria, administratively part of the Harem District of the Idlib Governorate. Qurqania is the administrative center of the Qurqania Subdistrict, which contained 13 localities with a collective population of 12,522 in 2004. According to the Syria Central Bureau of Statistics, Qurqania itself had a population of 2,050 in the 2004 census.
# Big Mishra Pedha

Big Mishra Pedha (also known as Mishra Peda) is a manufacturer of Indian sweets and snacks, headquartered in Hubli, Karnataka. Currently there are more than 50 branches in Hubli, and also in Gadag, Davanagere, Shimoga, Pune, Goa, etc.

## Background

Avadhbhihari Mishra is the founder of Mishra Pedha. When he moved to Dharwad in 1933, he initially produced Pedha in a small scale. His son Ganesh Mishra expanded the business & started producing Pedha in Hubli.
# Gursel Veli

Gursel Veli (Bulgarian: Гюрсел Вели Turkish: Veli Gürsel) (born 8 August 1982) is a Bulgarian football player of Turkish origin, currently playing for Vereya as a midfielder. Veli is an offensive midfielder. His first club was Maritsa Plovdiv. Between 2004 and 2006 he played for PFC Svetkavitsa and Spartak Plovdiv. Veli signed a 3 year deal with Lokomotiv Plovdiv after being released from Spartak Plovdiv in 2007. He was given the No.10 shirt. Veli made his official debut for Lokomotiv in a match against Marek Dupnitsa that was held on 22 April 2007. He played for 23 minutes. The result of the match was a 1:3 loss for Loko.
* Height - 1.76 m.
* Weight - 77 kg.
# Đỗ Thị Minh

Đỗ Thị Minh (born August 3, 1988) is a retired Vietnamese volleyball player, and a former member of the Vietnam women's national volleyball team.

## Career

Minh played the 2013/14 season with the Thai club Idea Khonkaen.

## Clubs

* Thông tin LVPB (2002–2017, 2018-2020)
* Idea Khonkaen (2013–2014)

## Awards
### Individual

* 2010 VTV International Cup "Most Valuable Player"

### Clubs

* 2005 Vietnam League - Champion, with Thông tin Liên Việt Post Bank
* 2006 Vietnam League - Champion, with Thông tin Liên Việt Post Bank
* 2008 Vietnam League - Champion, with Thông tin Liên Việt Post Bank
* 2009 Vietnam League - Runner-Up, with Thông tin Liên Việt Post Bank
* 2010 Vietnam League - Champion, with Thông tin Liên Việt Post Bank
* 2011 Vietnam League - Runner-Up, with Thông tin Liên Việt Post Bank
* 2012 Vietnam League - Champion, with Thông tin Liên Việt Post Bank
* 2013 Vietnam League - Champion, with Thông tin Liên Việt Post Bank
* 2014 Vietnam League - Champion, with Thông tin Liên Việt Post Bank
* 2015 Vietnam League - Champion, with Thông tin Liên Việt Post Bank
* 2016 Vietnam League - Runner-Up, with Thông tin Liên Việt Post Bank
* 2018 Vietnam League - Runner-Up, with Thông tin Liên Việt Post Bank
* 2019 Vietnam League - Champion, with Thông tin Liên Việt Post Bank
* 2020 Vietnam League - Champion, with Thông tin Liên Việt Post Bank
# Gras conjecture

In algebraic number theory, the Gras conjecture (Gras 1977) relates the p-parts of the Galois eigenspaces of an ideal class group to the group of global units modulo cyclotomic units. It was proved by Mazur & Wiles (1984) as a corollary of their work on the main conjecture of Iwasawa theory. Kolyvagin (1990) later gave a simpler proof using Euler systems. A version of the Gras conjecture applying to ray class groups was later proven by Timothy All.