oauth2/jws creates "invalid" signatures

[mi...@ubo.ro]

Does anyone know why the jws signatures created by the golang.org/x/oauth2/jws are displayed as "invalid signature" on jwt.io ? As far as I'm concerned it seems compliant with the JWS creation specs[0] but it looks like jwt.io is expecting a public key or "jwk string"  as well ?

Below is an example of signatures that appears as "invalid" on jwt.io [1] and the code[2]

[0]  https://openid.net/specs/draft-jones-json-web-signature-04.html#anchor5

[1] eyJhbGciOiJSUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJodHRwOi8vZ29vZ2xlLmNvbS8iLCJhdWQiOiIiLCJleHAiOjM2MTAsImlhdCI6MTB9.iIT1HnaZbpbN80TUunM_FAPgerBD4LilNZIX-M55tzRqgE8nDC57inkQF0KcVyLk4Y55WOtBlSj045u35twKkHokEGjSpSSQT31Rcf6ugxqYMKnqIvw9quzwaPJA_RmiudJVuCe_zyVka008M7fZfblwcaTWr1AXZ3iUrwOZnnP9Hli0merjPicVhNIG7SbZTyGFh6P9NUiX0y54iqsV_3yXQZep_UGJYuLR7v1hRRr1tphEiNUt4lBtcp_7nraLnUDTyMraZ8WpTwvn57GAQ4ShzxotEkR3z_5zDxsHRirJcLSBWZ-SNHl3XYXhGV48ePiMJlZ-PR6OQfJ35f-WiQ

[2]

https://go.dev/play/p/7fr-CxOIVvd

// You can edit this code!
// Click here and start typing.
package main

import (
    "crypto/rand"
    "crypto/rsa"
    "fmt"

    jws "golang.org/x/oauth2/jws"
)

func main() {
    header := &jws.Header{
        Algorithm: "RS256",
        Typ:       "JWT",
    }
    payload := &jws.ClaimSet{
        Iss: "http://google.com/",
        Aud: "",
        Exp: 3610,
        Iat: 10,
    }

    privateKey, err := rsa.GenerateKey(rand.Reader, 2048)
    if err != nil {
        panic(err)
    }

    token, err := jws.Encode(header, payload, privateKey)
    if err != nil {
        panic(err)
    }

    fmt.Println(token)
}